How to Solve By Completing the Square (NancyPi)

[@dylanmcconnell9939]

I love how she admitted straight away that the only reason were learning this is because our teachers made us

[@celsiusfahrenheit1176]

If you're gonna take calculus, it is very important

[@tiffaz84]

Does not make it true though. It helps when looking for the roots of quadratic functions when they are irrational numbers. That is instead of using the general quadratic formula.

[@mathfullyexplained]

Try my channel mathfullyexplained

[@999Aadil-Op]

You got 333 likes I won’t ruin it

[@mikehipparchusnewton7436]

It's important because it's derives the quadratic equation.

[@isaacsamuel9520]

Actually, she tells us the reason behind every step. My textbook says me to blindly do these steps and does not explain in detail. Thanks for this video!

[@yeetusimmafetus3782]

my textbook doesn't explain steps either, so it was a lifesaver to find her video

[@thorsteinj]

@okar ricardo ... or why having two answers (+/-) after squaring is important

[@JohnnySins69XO]

You sure it’s not because she’s hot

[@haretztj4682]

isnt that every god damn textbook?

[@mattheog1029]

Thorstein Johannessen Quadratic Equations/ expressions have 2 solutions. This is because when taking the square root of a number, for example, 25, 5 squared = 25 and -5 squared is also 25.

[@sawairaazhar4994]

How are all youtube teachers so much better than our own teacher?

[@Djzaamir]

because they love teaching, not like our teachers who prefer everything to be memorized by heart

[@linyousef9887]

Sawaira Azhar they’re not better xd but u wouldn’t be focusing in class as much as ur focusing in this video .. also being tired or bored in class gets u districted ..unlike being home and watching this video alone xd

[@woozihae]

ikrr

[@zacharyboeder7211]

It probably has more to do with the fact that watching this video is probably the second or third time you're trying to pick up this content. Usually this is what it takes to finally start learning something. You're teacher doesn't have the ability to "hand over" the ability to do a particular topic in math, rather its not until you decide to go out of your way to really attempt to learn something that you finally will.

[@omarceja3238]

@@zacharyboeder7211 Thank you every math video i watch has the same comment. Its like bro your teacher has to put the concept into your head first. Thats why you are suppose to study and practice. Looking up vids is literally a form of studying. XD sadly the majority of people speak before they put any though into what they are saying

[@alexiswaller700]

I like how she takes pauses to let me digest what she did and how she doesn't expect us to memorize everything. She's a good teacher. I wish she was my actual alg/trig teacher because my college professor could be a lot more helpful, especially with math but he doesn't care..

[@rashmit2366]

You have this in college? 😅 I am in 10th grade watching this

[@hexstealth7035]

@@rashmit2366 8th for me

[@Liztheb]

@@rashmit2366 This type of math follows you forever. I am a college grad coming back to re-learn that basics for the GRE. Never ends!

[@GongsBrandCube]

I am still fascinated by the fact she doesn't write backwards but instead writes on a window and mirrors it afterwards

[@mathfullyexplained]

Try my channel mathfullyexplained

[@seansasaki3861]

This video convinces me that everyone can learn math well if your teacher is qualified like Nancy Pi.

[@lightkira8396]

Simp

[@mathfullyexplained]

Try my channel mathfullyexplained

[@astronb6350]

@@lightkira8396 npc

[@swift9049]

@@lightkira8396 bruh

[@slimpickinses]

@@mathfullyexplained but she is easier on the eyes :)

[@electricdreamer]

One of the greatest mysteries of mankind is - how the hell does she write backwards?

[@a.ffirmative]

That's the question i have

[@xyz___ru]

the video is flipped

[@mohamedabayazid6040]

Jxshua Yuzn mirror board

[@jonathanwang7456]

She flipped it when she’s editing it...

[@rlewis1946]

I would rather believe Nancy makes magic happen in her videos.

[@enyafredericks9917]

I have been looking for DAYS to find an explanation on how to complete the square and this is the first one that I can fully comprehend and makes absolute sense. Thank you so much for taking the time to do this!

[@susiemurray8599]

guys stop simping for Nancy. she is very beautiful but she is a real person who can read the comments don't make her uncomfortable.

[@germanmata5946]

ok, thats a very good idea, but thats kind of hypocritical since you are the one simping.

[@mypussaenotyours4175]

but i just cant stop looking at her face instead of the numbers

[@mrman2293]

SIMPPPPPPP!

[@noughsubjectivity3686]

Simp

[@revolucion5398]

@@noughsubjectivity3686 baruch hashem

[@jennaschulman4957]

I am failing pre calculus right now . I just wanted to let you know you saved my life

[@mathfullyexplained]

Try my channel mathfullyexplained. Many topics that can help you

[@jasonruzicka7954]

but still failing calculus ;)

[@Nat71195]

i don't understand why when my professor was trying to teach this to the class, everyone including myself were very lost. You made it so much simpler. Thank you! Wish me luck on my exam guys.

[@pianodude5358]

Good luck:)

[@Theknowncerealkiller]

What happened with your exam? 😁

[@tobyf6414]

@@Theknowncerealkiller lol

[@neverpresent]

What happened!!!

[@Nat71195]

Took me like 5 mins to find this comment since I seen the replies but when I clicked on the them it didn’t direct me to my actual comment. I PASSED, in your face whoever thought i failed. Buahahhaha. You speak words into existence. 😉 say you will pass and you will !

[@laneyb8911]

Currently practicing for the SAT but I haven't taken a math class in like 7 years. The study guide does not give good explanations. Your videos are a lifesaver thank youuuu

[@mathfullyexplained]

Try my channel mathfullyexplained.

[@1958vintage]

I think the main reason that Nancy is quite successful here is that she sets out why she is taking the steps she does (as some have mentioned). As a Math(s) teacher myself, I think another reason why some of those of you who have commented here think it's easier to learn by watching a video is that, in class, the teacher is often distracted by disruptive pupils who try to make a game of stopping the learning process because they don't want to be there in class. If you've taken the trouble to look this up on the internet then you've already invested some effort yourself, and you'll take more interest in what's happening, and you won't have competing distractions either.

[@peterbradshaw8018]

I was doing a one and one tutorial with a student who thought he could watch Manchester United play while I explained this to him. Yep we have multitasking students of that calibre. The father who was paying for the sessions was irate when I told him about the incident.

[@wodeyaeric5351]

that's true but some teachers basically don't comprehend the concept itself.

[@jameskerr514]

I appreciate that you didn't try to factor out the leading coefficient and instead just divided everything by it. That's the way I teach my students and this is the first video I found that explained it how I teach it. Good work!!

[@WellingtonMSB]

Miss NancyPi I missed out on med school because, in high school, I didn't have a math teacher like you. I've decided to watch each one of your tutorials and conquer this beast that got in my way. Thank you

[@jasonqin6009]

who is watching this video the night before the test xd

[@bebnick88]

W

[@Kdivinity_]

Me 😂😂

[@Suraj_makker]

Me

[@khadijabutt7255]

Tomorrow is my final exams and I start learning it now 🤣🤣🤣thanks Nancy 🥰

[@TheElectricSoda]

I have to do a retest

[@KitKat-gn2nn]

Quadratic formula for axis of symmetry: -b/2a Completing square x: (b/2)^2

[@IceCreamMilkshake777]

Words can't express how this was way simpler than how my teacher explained it

[@sarahwatson7692]

michaela menzel That is a common problem in math classes. Having a teaching degree in math does not mean the person can teach the subject and most math teachers cannot teach well. The ability to teach is innate in some people but few go into teaching of any kind. My math teachers were at a loss to understand why I could not grasp the material as it was so simple for them. Everything you see her writing is pure gibberish to me to this day.

[@lightkira8396]

Simp

[@SaifulIslam-uu9xz]

My teachers showed me a mucchhhhh easier way for the first situation. You basically do what numbers multiply to make -7 which is either -1x7 or 1x-7. Then you choose between them sums and do which of those numbers add up to make 6 and you’d choose the -1x7 since -1+7=6. Soooooo simple this way. Nvm I realised this only works in some situations there’s a different method too hard for me to explain

[@sunnyzhu5791]

@@SaifulIslam-uu9xz your method called crossing method

[@therandomizer5972]

m learning a lot of things from here which i couldnt understand from my mam

[@Viick21-sp4yl]

My first language isn't english but i was looking for math classes in english, bc it's easier for me to focus, then i found this channel and loved it

[@wallygoots]

The usefulness of this is that most quadratics do not cross the x-axis at nice integer values. Factoring only works with nice values (no fractions or decimals), but completing the square and quad formula solve all quadratics including those that don't cross the x axis at all (2 solutions in the imaginary number system). I prefer completing the square to quad formula when a=1 (no coefficient other than 1 on x² term). Usually it's just add b² to both sides and simplify with a square root. Same solutions as quad formula and I think more efficient (unless we can use a spreadsheet just to enter a, b, and c). Oh, and completing the square is really valuable for other things like graphing conics.

[@Mehraj_IITKGP]

If you notice carefully, she is teaching us how to complete the squae.

[@alissamerz4648]

Easily the best video I've found on KZbin explaining this subject. Thanks for the refresher so I can pass the tests necessary for my elementary teaching credential :)

[@kanankanan8120]

Her smile after each step simply kills me

[@hashim_iraq]

haha

[@lightkira8396]

Simp

[@mark9606]

ik like why she look like she tryna flirt with us?

[@brighamsankar6024]

Simp

[@xavier810]

down bad

[@abukarmurudimumin253]

This is a good teacher who made us understand math lessons; therefore, anyone who abuses her won't learn math deeply! Respect her because she is teaching her knowledge to other needy people! Really,how I understood math from her even I didn't comprehend my school teachers as well! Thank you Nancy, the greatest math teacher I have ever seen in my life time!

[@nickcellino1503]

What a brilliant concept. The math teacher is a gorgeous woman so someone found a way for her to face the camera 100% of time while she's writing so we can admire her beauty and her brains simultaneously. Sheer genius.

[@views-dz7cg]

Nancy tryna teach 12 year old boys online: Loooorrrdd forgive me for what I'm boutta do

[@AriT105]

I think their is a specific website for that?...

[@cgkty5315]

Raul Tapia club penguin ?

[@shobarbaba]

Why will 12 year olds search up how to find completing the square tho?? Aren’t they a little small to do that ? ? ?

[@AriT105]

CGK Ty sure 💀

[@iknowyouseeme3233]

@@shobarbaba isnt algebra 1 8th and 9th grade math?

[@Nishaaat]

This is so beneficial am in grade 10 and my teacher takes 1 week to explain the whole sum nicely but here in a short period of time i get it correctly in my head.I have an exam tomorrow and this is very beneficial.Thank you NancyPi

[@SigmaWarzoneAlpha]

algebra 1 is a 9th grade course??

[@aiuoe2]

@@SigmaWarzoneAlpha How can you assume that everyone watching this video are from US ? May be he's from a different country where Math is 'Math'; not divided by courses like Algebra1, Geometry, Algebra2 alike UK.

[@paulhemming5376]

@@SigmaWarzoneAlpha what's in class 10th algebra just asking from a different country

[@barryallen9465]

maybe or he may be in a country that is simply behind lol:Like africa or the philipenes.@@aiuoe2

[@bcandidvisuals]

This was really a nightmare for me, thanks for explaining the steps slowly and step by step and also explaining why things go where they go and not just assuming the viewer knows! More videos. This helped a lot!

[@parahjapheth7920]

Just the best video I've watched on completing the squares method of solving quadratic equations. It's all made simple. I appreciate you giving different situations, and the approach to take. Thank you.

[@bluestarindustrialarts7712]

I listen to these vids for ASMR relaxation. So soothing.

[@MrTalseti5]

The “Matrix-like bullet-time” effect of your speech is perfect for complex subject like this. Wish I had this 40 years ago.

[@rayg.4924]

Thank you so much! I am in Precalc rn, and I haven't used this method in a long time but you refreshed my memory by explaining it really well!

[@mathwhisperer490]

I think it's great that Nancy tells us that there are other, maybe better, ways to solve the equation! But of course, students still have to learn this method. Personally, I like the method, but that is personal preference. Great job, Nancy!

[@_na11talie76]

This explanation is the best I saw on KZbin

[@Liztheb]

I watched 3 different videos before I found yours. Thank you for not skipping steps and clearly explaining why we must perform each one. Yours finally helped me!

[@bg1unidentified]

Thank you for this video. I was having a huge issue with this method because the steps are laid out but never explained like you explained them and now it makes sense. I still don't like using this method because the quadratic formula is my favorite method oddly enough, but since I have to do it, at least it feels less intimidating now.

[@johnholme783]

Great mathematics learning resource! Both simple to understand and comprehensive! Thanks a million nancypi!

[@dennisrendfrey5636]

Again your my go to person when I need to learn something!! I tested into college level algebra, I'm now in pre-calculus and I've never learned this. My class mates have done this in high school. Thank you again !!! This will make my Math Journey much easier. I'm 68 years young and enjoying college!!!

[@brighamsankar6024]

OK boomer

[@aiuoe2]

@@brighamsankar6024 Bri-sh ppl...

[@seungmoo4131]

@@brighamsankar6024 wth..??

[@seungmoo4131]

@@aiuoe2 what does that have to do with this?

[@aiuoe2]

@@seungmoo4131 you are too yng

[@Steven-wv1he]

The most GORGEOUS math genius!!!!

[@RupertBruce]

For your amusement, skip to @7:30 and set it to play at half speed: )

[@clarkgrayhame1250]

Wow I just love how you teach these things so well. Your instructions are easy to follow and you make sense out if it. Thanks for your videos.

[@feero9680]

When the test is about drawing a curve, i prefer using completing the square to solve the quadratic eqn given. Bcos i can find the vector(max or min coordinate) and where it intersects the x-axis. Both just in one go. And of course another great video!

[@texasnewt]

Right, completing the square results in an equivalent equation that is more graph user friendly.

[@rickeyestes6937]

That was a good video Nancy. You explained that clearly, concisely and make it look 5th grade.

[@realdvgarg]

It is 5th grade math.

[@anugrahahaha1908]

@@realdvgarg ig for indian schools....

[@realdvgarg]

@@anugrahahaha1908 Definitely for IB schools

[@anugrahahaha1908]

@@realdvgarg ohh

[@nomad-1776]

I watched 3 videos before this and none of them did it for me. This video breaks it down nicely and I feel like I have a decent understanding of it now. Thanks for the video.

[@RobertMStFleur]

Best math teacher in the world is Nancy

[@radioactivemilksheik7010]

THANK YOU SOOOOO MUCH ! I've been struggling with this for over year and you taught me it in less than 20 minutes

[@joshuapierce17]

same

[@eslamsaeed8395]

You are amazing I don't understand English good But now I understand what do you say Because your explain easy and you speak slowly It's so good Thank you

[@ViratKohli-jj3wj]

Ok Muslim

[@PM-vb4od]

I like the speed she talks. A lot of teachers talk like they have drank too much coffee.

[@gotnextventures2228]

The online lessons I do on flvs aren’t the best at teaching step by step and explaining it like this, so this video has already helped a lot for me

[@FrankCordovaMileHighBorn]

Man, in the near 20 minutes watching the video, I learned more from you than when I was in grade school and college.

[@stringofpeas]

thank you so much for leaving out all of the bull and getting right to the point. This was clean and easy to follow

[@sanguinj]

Great Nancy. I wish you had been my algebra teacher 50 years ago. So clear !Keep doing this work !!!

[@cmichael40]

ditto.

[@Bruce-bz3ke]

Unc why are you watching this you’re high school days are over

[@MiniMuskCoin]

@@Bruce-bz3ke fr wtf 😭

[@theshadypersonify]

Nancy It won't be long now for my nomination for my nobel prize. Something that I would like to inform you about is that I use a blue light fliter on my monitor ( called Iris) and wear glasses that block blue light to stop eye damage and preserve circadian rhythem function. So when you use the color red it is almost invisible when I watch your videos at 2 in the morning. I love your videos Thank you :)

[@Lionheart683]

The real question would be what kind of circadian cycle is preserving watching videos at 2am?

[@MajRatbag]

Shutup Sheldon Cooper

[@brighamsankar6024]

@@MajRatbag lmao bro

[@coolbeans9771]

OMG. Best video on KZbin. Thanks man!

[@juridicalbike344]

the part where the factor was half of bx was not taught to us at all, you are a lifesaver Nancy!

[@stevenwilliams2031]

The most gorgeous mathematician of all times.

[@angel.gutzzz]

The fact that nacy did this even tho she knew it wasn't important just speaks to me.

[@mathfullyexplained]

Try my channel mathfullyexplained

[@surajvarne3992]

hey Nana, beautiful the method you showed us but what about a sum like x2+4=6X

[@danieljensen6154]

I’m guessing the x2 is a square, legit minus 6x from both sides which gives you x^2-6x+4, (the way I do it is different but) x^2-6x+(6/2)^2-(6/2)^2+4=0 then simplify from there I cbf

[@Neerajyadav_ind]

Wrong hai Q3 last step X2+6x=7

[@DesertRosePro]

Thanks Nancy, couldn't make heads or tails of Sal Khan's explanation but you made it clear as a bell... like always.

[@shiyeon9516]

Why am I paying so much for me to look up youtube more than half the time. Thank you, this really helped me (as someone with learning disabilities as well) super thorough and no room for "but or ifs".

[@dikkebmw436]

Watching this 20 minutes before the test. Wish me luck.

[@mathfullyexplained]

Try my channel mathfullyexplained

[@dikkebmw436]

@@mathfullyexplained I will sir!

[@johnmapomajr7551]

If this was my math lecturer I would never miss math classes💀😂😂

[@raihat4018]

😂😂

[@glorygloryhallelujah]

The hair flip gets me every time

[@searedsalmon4952]

She looks so done and enthusiastic at the same time I love this

[@mariustone11]

This is so much better explained than any text or teacher at school, amazing.

[@smartingamerica]

Well done - concise and complete for basic purposes. Thank you!

[@mohammadammadameen8834]

I would never miss my class if i had such a beautiful maths teacher

[@roccovitiello8036]

Why does Nancy look like she’s about to have a mental breakdown?

[@CALISUPERSPORT]

I dont know but it's really hot

[@elpatoendrogado4005]

lmao

[@logiic8835]

Norcal what

[@Distillations21]

Norcal 😂😂😂😂😂😂. Atleast your not lying she’s cute af

[@mkidd8806]

May she had the breakdown and this is the outcome

[@Daves_Cave]

I tried about 6 different sources to try and understand this where x^2 has a co-efficient >1 ... yours is the only method that I actually understand - very well done 🙂

[@apothe6]

Having such a deep knowledge on why and how math works is so important, I am really learning from you

[@zacharynoragon4030]

nobody going to talk about how she's writing backwards?

[@fizanaliteach2833]

Same

[@thedaigles6034]

Easy peasy. She recorded the video then she flipped it when she uploaded the video. Made it look like she is writing backward.

[@mathfullyexplained]

Try my channel mathfullyexplained

[@Eterrath]

Halfway through the video I just realised I was looking at her the whole time. I feel like a creep.

[@pejajapeepeepee6417]

Me too

[@chrisrios802]

I did the same but only realized when I slowed the video down

[@A-Jams]

no problem she is hot. I wish she was my teacher then I might give a damn

[@RIZZAcademy101]

@@A-Jams 🤣💀

[@A-Jams]

@@levirosner1728 chill bruh, he’s saying why looking at her than learning math

[@Roxy_Vision]

Everyone: Cant stop looking at Nancy and not learning anything Me a Gay: Im 1000 lightyears ahead of you.

[@glowingsquid496]

She's so honest i love her 😭😭

[@seanhunter111]

Generally the benefit of completing the square is that you get the formula in a form where you can see the coordinates of the vertex of the parabola (eg if you have y=3(x-2)^2+3 your vertex is at (2,3), so things like understanding the translations you use to generate the graph from the graph of y=x^2 are easy. Secondly if you know how to complete the square you also are able to derive (and understand the derivation of) the quadratic formula. Once you know/understand that, for solving, the quadratic formula is strictly better than completing the square. But if you have to sketch the graph you might as well complete the square because it makes sketching the graph easy and then having completed the square you might as well solve that way.

[@transrightspanda]

aw you seem so nervous it's adorable. this video was a help thanks!

[@davidbolduc7131]

this was way more helpful than MyMathlab video. Thank you Nancy.

[@lindsmhako1288]

the easiest method ever, South Africa Approves.

[@gracedell]

thank you!!!!! I wasn't sure what number to put for the perfect square and you were the only one who said it.

[@victorekenta-ifeanyi807]

This video took me from not understanding completing the square method at all to it becoming my favourite method to use

[@3bbad]

i like the pink numbers!

[@chandrakumar4479]

Me too

[@JustusMJoe]

@@chandrakumar4479 question (2) answer, why we do not add the negative sin to the 5?

[@lachlanwoodworth201]

Blink twice if you are being held hostage

[@dhadbaoui]

You give a shortcut for how to get the answer, but completely skip over understanding the math itself. How do you factor it out? Then, alternatively show the short cut.

[@Vikermajit]

Awesome tutoring, Teacher Nancy. Everything explained so well, step by step...Tqvm.

[@chrisp2639]

Currently learning trig sub in Calculus 2 and having to come back to this for simplification. Thank you for making this!

[@babyboyk]

Am I tripping or did she not finish up question 3??

[@kimberlydell2806]

She didn't sadly. I think she wanted us to be able to solve the last steps as they were they same.

[@jj6321]

i got x+3=+-4

[@juanserna5324]

once she gets to the x^2 + 6x = 7, the rest is just like example 1 she did earlier in the video

[@RealSlavGod]

I am in university for engineering and I don't even know how to do this lmfao

[@mitchhall1284]

Same bro

[@mirkoramphul5898]

How did you even get into course?

[@maxsun3368]

@twistedblktrekie Because you don't really need to know this for higher math

[@ollieparsons3113]

Electronic engineering degree but same lol

[@peterjeffrey8126]

same bro, same lol

[@ahmadabdulrahman3838]

I always hated math but you am OK

[@mikeoliver5671]

The following assumes that students can identify a perfect square, when the coefficient of x^2 is 1, ie --- it has three terms --- the first and third terms are perfect squares, and --- (1/2 the coefficient of x)^2 = the third term. eg for x^2 - 4x + 4, tick, tick, tick (-4/2)^2 = 4, as above. In the case of x^2 + 6x - 7 = 0, students need to know what that equation MEANS. It occurs when y = x^2 + 6x - 7 is = 0. GEOMETRICALLY that occurs when the graph of y = x^2 + 6x - 7 cuts the X-axis (which is the line y = 0. y = 0, so x^2 + 6x - 7 = 0 😊 and that tells us if the graph cuts/touches the X-axis, or not)) My objection to completing the square on x^2 + 6x - 7= 0 is that the quadratic x^2 + 6x - 7 can be factorised. x^2 + 6x - 7 = 0 (x - 1)(x + 7) = 0, and so on. Anyway, dealing with it as it is: x^2 + 6x - 7 = 0, the first two terms (x^2 + 6x) have "the makings" of a perfect square. If it WAS a perfect square, it'd be x^2 + 6x +9, from the above. As you point out, the +9 comes from (half the coeff. of x)^2, when the coefficient of x^2 is 1. I say to myself, "It'd be nice if I had (x^2 + 6x +9), which is (x + 3)^2" So, I behave as if I HAVE the perfect square ie x^2 + 6x +9, then to 'balance' the +9 I have added, I subtract 9, then the original -7 from the start ==> x^2 + 6x +9 -9 -7 = 0, then I put a bracket around the first 3 terms (x^2 + 6x +9) -9 -7 = 0, then transpose the -9-7 (-16) (x^2 + 6x +9) = 16 (x + 3)^2 = 16, then solve as you have. Potato/Potahto, right?

[@ritikamishra4083]

Hi Miss. Nancy I am from India you explain very well this such a confusing completing square method you are great 😎

[@rollseyes286]

She was using Black and Pink pens My mind: Blackpink in your area!!

[@whatisabias2652]

pepper 'n' salt cringe

[@user-kt9ul5kq6x]

Cancer

[@soheelmahmoodsagri2823]

Mee too😁

[@Scarabola]

I KNOW THE FIRST THREE NUMBERS

[@sana2125]

YESSSSSS another STAn same tho

[@RustyRustacean]

No one is asking the important question: How does she talk from behind a glass? xD

[@matarmbe5604]

easy

[@AftabKhan-bz5yd]

Microphone man

[@sexyarmpit3915]

and writing with a left hand and backwards LOLOLOL

[@aydenkreiss4298]

@@sexyarmpit3915 It's mirrored lol

[@Ben.N]

Segways almost as smooth as Linus.

[@oscarmullan8237]

Segue

[@OpticalMessiah]

As a retired professor, I'm impressed in how Nancy is handling this tricky material. The explanation is outstanding. Also, us sinistrals are very happy that she's left-handed and very capable with this material.

[@malikadnan3081]

MISS NANCY YOUR STUDY METHOD IS SO AWESOME...THANKS

[@mrgatogris8863]

First this video was super helpful. Second. You are beautiful 😍

[@slimesdesigns7004]

ok

[@jasonalbers5578]

nice guy?

[@minty2826]

Perv

[@admitonee1668]

@@minty2826 tell me why i see you in every comment that is complimenting nancy on her looks and on every single one of them you comment "perv"

[@ViratKohli-jj3wj]

@@admitonee1668 perv

[@yazxn8536]

I like how no comment is about the lesson including mine lol

[@Seizuqi]

why are you facing the camera sideways, like dreams face reveal

[@ryanchiew4353]

lmaooooo

[@notengonombre_]

oh lol

[@dementormond3740]

I like how she makes everything so clear ❤

[@N4SX]

Nancy, your presentations are awesome. I use your video's to teach my grandsons math. You are a credit to MIT.... Allan S, MIT class of 1962