Completing the square

[@xkilla911]

i like how this video's resolution itself is a square

[@n6nno135]

mans is struggling and still putting out this content

[@mattgilbert837]

200th like

[@tiaraashley1]

I have literally been trying to figure out how to do this for about 3 years. You just made it all freaking clear just ugh I love you.

[@kamabokogonpachiro6797]

hey after 8 yrs

[@tfr]

@@kamabokogonpachiro6797 hey after 3 months

[@kamabokogonpachiro6797]

@@tfr hey after 34 mins

[@valhalla1515]

@@kamabokogonpachiro6797 hey after 13 mins

[@kamabokogonpachiro6797]

@@valhalla1515 hey after 57 mins

[@thomasmuller6050]

Khan Academy is a life saver

[@HeyKevinYT]

Who isn't watching this in 2008

[@komickid833]

Kevin vs. Gamingz me

[@braxtonclanton8517]

Dang sal, you know your stuff. You should be a teacher at my school (Heaven knows we need a math teacher who explains things well). Thanks for the video and God bless.

[@nuh433]

Can we have remasters of some of your older videos?

[@watrutledge4766]

Dude you just saved my life I have a test on quadratic equations tomorrow and I had no idea what it was so I searched on KZbin and found this and now I 100% understand it. Thank you so much

[@justadumb8864]

How did you do on your test

[@loganyashchyshyn9065]

Yeah

[@filipjaworski]

you explained in 14 minutes what my teacher couldn't for 4 classes!!! thanks!

[@iSVX1103]

Hey 11 year old comment!

[@yKreepzz]

You guys deserve a noble peace award. The amount of fights you have prevented due to people being stressed from maths would be phenomenal. Thanks heaps! :)

[@nagarjunprasad]

I am in class 12 now (grade 12 for you Americans) and it took me this much time to realize that when a number is shifted across equals sign,we are just adding its counter part both sides!

[@efisgpr]

actually, Canadians say "grade 12", but Americans say "12th grade"....also, Australians say "year 12".

[@richter4446]

Adding on about Australia we also call 6th grade "grade 6" and/or "year 6" but then when you reached "7th grade" we just call everything "year 7,8,9....."

[@efisgpr]

Thanks, Derek, how interesting. :)

[@callofmariocoinops]

The "you americans" part was unnecessary. Remember where this site was invented???

[@VoVina111]

+Te Amasin Spoderman lol Didn't realize he/she calling us Americans was an insult. O.o

[@jjwise12345]

Literally didn’t understand what the hell my teacher was talking about and have a quiz today on it, thanks

[@aubreyroberts686]

Killer90x same

[@big4headedGangster]

This is so confusing that I started admiring my reflection for the first time.

[@markgarau]

You dont know how much I love your videos... they help sooo much. Thank YOu.

[@SharsOasis]

The best explanation of Completing the Square I have found! Thanks so much for this and for all of your other videos.

[@iSVX1103]

Hey 10 year old comment!

[@king-bg4rp]

​@@iSVX1103hey three year old comment

[@iSVX1103]

@@king-bg4rp time flies by fr

[@TheFuggin]

Once again, you save my life. I just feel like I have to thank you. Thank you so much!

[@ladislousfarawadya5115]

khan academy is actually amazing.....what gud lessons....to be hinest they xplain things in a much simplified way that makes even a student like me understand.. hope you will be making more videos.....

[@BHkpopfan]

this is really helpful since the teachers in my school dont teach us just give us the work and unit and the textbook doesnt explain properly...they expect us to do everythinng ourselves and its really confusing. but this clreared some up thanks

[@alexanderslasynski8340]

B H recently it has seemed that my teacher is actively setting some students up for failure she will only answer the questions that some students have and is playing favourites towards them, khan academy has been a better teacher for me in answering my questions than she has

[@YoshiAsk]

Yeah, some of my teachers do the same thing.Especially now that Common Core is a thing, a lot of the teachers don't understand the content and the "textbooks" don't explain it anymore. The books are really just workbooks.

[@Christian-gj4uw]

Yoshi Askharoun or sometimes they show us an easy example but then when I have to do homework, the questions are a bit more complex and feature certain things that he originally never explained.

[@YoshiAsk]

Yup.

[@mecha249vlogs]

Unpopular opinion: I love common core because I don't do my assignments at home out of procastination, it lets me do the whole thing without the help of the teacher because I find my own formulas and solutions using the book, and do it all in the middle of class while ignoring the teacher.

[@joedoyle8745]

Took my teacher 2 weeks to get through this shit and I still didn't get it, but Khan University manages to make me completely understand it in 13 minutes...my teacher sucks smh

[@lespoon5392]

Joe Doyle my teacher hasn't even been in class all last week, and since the subs were LITERALLY DOING NOTHING the entire class and I have been having to try to teach ourselves how to do this crap. Let's just say, I really hate having to try to work on this over spring break

[@spinodino9563]

Howd it go

[@zerolizard]

There must be a math conspiracy going on because, out of all the math teachers I have had, you are the best! Plus you are not seeking financial gain by charging for your videos so I have the highest respect for you. You are helping a lot of people. Thanks.

[@omarz2145]

Wow when I asked my professor why she was dividing the coefficient of the second term by 2 she just said because that's how it is. This explanation made things so much clearer for me. Thanks.

[@DeathsTacoIsHere]

My teacher doesn’t know how to teach, I’m lucky enough that she told me the name of the method so i could actually learn to do it online, thanks Khan Academy

[@Craft1man]

This acutally helped me prepare for my test. Keep up the great work!

[@justadumb8864]

How'd you do on your test

[@pavindudiaz3094]

You save my life always. I don't need tutition anymore!! Thanks Khan Academy!

[@Seansaighdeoir]

Sal - you are truly a great human being!! God bless you for these videos.

[@rexiota7544]

Omg! No one in the world made it clear to me but u did it with logic! Thanks a lot brother!

[@supercarnitas]

I haven't taken a math class in three years and now I'm taking one in college and I'm really watching all his videos on algebra just to refresh my memory.

[@greenec336]

I'm in eight grade and ending the painful year of algebra, and khan academy has been there for every concept i didn't understand, and even things i didnt know i needed help on. it significantly raised my test grades and stopped me struggling with math. thanks ! :)

[@BLT1538]

thank you for the help its always easier when someone explains for you rather than the text book

[@Bagelmut]

If it wasn't for this shit, I'd be failing Pre-Calc

[@Chaoticgoldfish]

I low key just watched a shit ton of this vids for my final tomorrow. I have a d- in pre cal

[@MX-hu9qy]

how did it go?

[@MX-hu9qy]

y tho

[@tia6986]

Me asf

[@DAtNizzaYOuKnOw]

I appreciate ppl like you who take the time to explain things like this so I can understand it better.Thanx man!!!!!

[@iSVX1103]

Hey 12 year old comment!

[@CreepyGeorgie]

This made zero sense to me and my class is testing on it so I figured why not watch this. I actually get it now and am able to do it on my own. I really appreciate this, thank you so much! :-)

[@Licona1219]

You have no idea how helpful this has been to me. Thank you SO much! I'm now subscribed, of course!

[@king-bg4rp]

yooo are you still alive

[@Halo2maniaccc]

THANK YOU!!! I needed to review for my exams tomorrow and my notes are complete junk as are teacher has no note taking structure this helps so much. Again thank you very much!

[@chiGuy7575]

This is explained in such a good way. the way my teacher explained it was so confusing. the 2ax way of teaching it is so much easier. very helpful!

[@firehand1011]

SAL, without your help i wouldn't stand a chance in maths. GOD BLESS YOU

[@scream1421]

thank you so much im a sophomore in high school and this helped me so much Khan Academy has always helped me whenever i need it.

[@JeanMariene23]

Thank you for explaining this so clearly! Finally someone who knows how to teach!! I wish you were my teacher :-)

[@anomqween]

YOU ARE AWESOME. Thanks for taking time & uploading this!

[@iSVX1103]

Hey 10 year old comment!

[@Anrich]

Yeah, that's the pure truth. I did very well in high school maths, and the only reason for that was the fact that my teacher explained exactly why each step is performed when calculating something, and exactly why a certain formula works to calculate something. Once you know the why, the rest a practicing, and then a distinction :)

[@thelostbobby7]

i love you thanks for making these free videos u really are a life saver!!! :)

[@Jaknalyric]

You're an amazing teacher. Thanks so much!

[@05swanbe]

I'm having to do my AS C1 and C2 maths on my own at home just learning from the book. I'm so glad I found these vids! Thankyou!

[@nickkarantzoulidis682]

thank you for teaching me pre calc better than my high school teacher could

[@Tehhunter1]

I'm preparing for my Math IB exam (in about 5 days) and this has saved me time. I don't have a teacher at my disposal atm, so this was quite effective at teaching me what I needed to know from the syllabus. Thanks bro, you're a credit to the world.

[@hasaanqadri2813]

best online video channel. extremely helpful thank you very much

[@misinterpretations]

THANKYOUSOMUCH. My grades have been dropping horrible in algebra 2, in no small part to my atrocious teacher, and this video helped me understand completing the square so much better. This video (in conjunction with the Yay Math! video for completing the square) was more informative than periods and periods of my class.

[@davidoneill2466]

An easier way to grasp completing the square is to visualize the quadratic equation geometrically. x(x+a) makes a rectangle with one side distance x and the other x+a. x+a = x+a/2 +a/2 now make the square (x+a/2)(x+a/2) This visual approach is way easier for a beginner algebra student to understand where the (a/2) squared = a square/4 comes from

[@blasemmanuelvillarino1754]

When you already know the lcd of those denominator you have then to divide it to the denominator of every fraction times it's numerator so that's why we have 72 ;)

[@sabrinaraasin8543]

Yeah i still cant over that part

[@blasemmanuelvillarino1754]

@sabrinaraasin8543 practice will get you there

[@Diamanttii]

thanks, I finally understood it, most of my classmates didn´t understand it from teacher´s explanation and me neither, but today I took re-exam and suceeded!

[@rocknsg91]

I hate how good you are at explaining this. I'm changing my major now. Arbitrarily, of course.

[@Sasha7amad]

THANK YOU A MILLION! through out this year ive been applying the formula without knowing what am doing! i used to get confused while solving! ive got an AS exam in a couple of days

[@Seattle206723]

The Man once again! Thank you for this explanation. I took this in the summer and we didn't complete the last chapter. We ran out of time in class.

[@benjisamosa6060]

At 7:26 did you change the +3 to -3 and the -19 to +19 just because you worked it out that (x-3)(x+19) works in the equation or do you always have to do the reverse the the results when putting them back into brackets please?

[@qystinad.8877]

+MegaBenGaming if x=3 then when you move the 3 over to the same side as x it becomes x-3=0

[@benjisamosa6060]

Qystina D. ok thank you

[@wangzhihuang897]

Ur videos really help me, keep up the good work Khan Academy! :)

[@JBD7DramaQueen]

I CANT DESCRIBE HOW AWSOME YOU ARE! MY RESPECTS!

[@jordanmiller6024]

Thank you so much. My math class is very big so I do not get the chance to go at my own pace and get that teacher to student feel. Thank you so much!!!! l

[@NoOne-sy5fg]

i love you dude you deserve a Nobel prize for this

[@SHWAPAH]

.....HOW CAN YOU HAVE SO MUCH KNOWLEDGE ACROSS SO MANY SUBJECTS?? 'TIS AMAZING!

[@j822bosh]

I am studying this for a test and I like the way you explain this. I knew from my class you ad the second coefficient divided by 2 squared to both sides of the equation but my book or my teacher explained the x squared +2ax + A squared relationship. To much is implied assumed knowledge. Your clarity helps illustrates fundamental mathematical relationships which helps improve my critical thinking skills. Kudos

[@gordonsph]

thanks a lot Khan Academy! 13min n I figured it out. Life Saver for sure.

[@SathvickSatish]

Wow! Thank You so much Salman Khan!!! You helped me a lot! May God bless you!

[@Griffinfit92]

Dude you are amazing. God of teaching

[@crustythethird3284]

im not gonna remember any of this haha

[@danijelblair9087]

fr tho did you?

[@ninefyre]

Did you tho

[@spinodino9563]

Friendly reminder to tell if you remembered

[@RockstarPatches]

I was bored last night and came up with a much simpler and more direct way to complete the square. The good thing about my way is you don't have to manipulate that first term to make it have a coefficient of one. It's really straightforward. First term will be square root of coefficient of x^2 and the other will be coefficient of the x divided by twice the square root of that same x^2 coefficient. Squaring that last number then gives what you need to add to both sides...

[@antonnig4288]

If needing to use khan academy makes me dumb, I’m proud to be dumb

[@ferrarimad0]

i also got my maths gcse tomorrow completing the square was probly the only thing i had huge trouble with so thanks for your help

[@TricaPLeeAnn]

i kinda get it now.... this one explained it a lot better than other videos on youtube.

[@janderson2494]

You're a goddamn savior, Sal

[@ilonawinn4256]

Thank you very much for your video! It was very visual and helpful!

[@anilmewada1322]

hello

[@lilbabyangel125]

so helpful! this way is much easier than what i was taught!!

[@TrooperSteve147]

You the Man bro! definitely better than my teacher by far!

[@SovietLlamaMC]

My algebra EOC is next wednesday. Thanks for refreshing my memory!

[@kathleenivy41]

Thank you so much .You are a freaking lifesaver THANK YOU

[@vibrantrokrfan24]

Thanks. This makes a lot more sense to me.

[@IMBLUESTREAK23]

Wow, you explained that a lot better than my foreign TA. THX!!

[@luciasetlhomo358]

thank u it ws so simple nd clear

[@TheVOIDaccount]

I love this man.

[@namelessking8419]

What careers/professions use completing the squared method?

[@elainevillanueva1087]

Thank you for making it simple. :)

[@Uncausedspark]

Thx you taught me better then my math teacher in 10 minutes

[@Djcrazykidd]

Thanks Man ,That helped a lot . Seriously man thanks.

[@budgiebreder]

6:18 that light blue square root step is the one i always forget thx now i'll remember this video to help me get the ans!

[@abeNpdx]

That's why I love Sal at the Khan Academy web site ....I get hung up when I don't understand why...and that's what Sal does on almost all his vid. He tells you why which gives you context...and with context as a back drop...it all comes into focus for me. KhanAcademy web site is so helpful!

[@serprex]

Finally a proper explanation. Schooling has it with everything being done on the left side (ends up pretty unintuitive) so I find myself just using the quadratic equation and -b/2a to dodge those questions As for proofs, you only have videos showing the quadratic equation with examples. No real proofs of it or anything

[@XItsTheQuenchiestX]

Made my math homework so much easier! Thanks

[@AlaskaKace]

Always a fantastic job!! Thanks!! =)

[@Dii1888]

Sal u are just amazing man luv u bro! :)

[@kaitlyn1230]

he makes it way harder then it should be

[@restitutororbis964]

He is explaining the full concept unlike some teachers that miss the most important parts of a lesson.

[@rwilhelm7]

amazing, my teacher doesnt teach and you helped a ton!

[@goldfishi5776]

I want to use these things in daily life because math is beautiful. Sal please help!

[@maanram001]

thank you for the big help! you're a great teacher! :)

[@marcosnunez2955]

This guy is awesome he teaches better than my teacher

[@zinniahenjum9948]

Thank you so so much. You saved me!!!!

[@Smrtification]

That was really great, thank you SO much. You should do a video on what happens if you have a number in front of the x though. EX: 0.5(x^+12) +2

[@Juxtaroberto]

@moopy239 It's exactly what it sounds like. You're turning a trinomial from one with funky numbers, into one that is a perfect square. i.e. 16 is a perfect square, because 4^2 is 16. Likewise, a^2+2ab+b^2 is ALSO a perfect square, because it equals (a+b)^2.

[@أروىالبدوى-ي9ر]

Thanks alot really appreciate your help 😊

[@PeteDork]

Much better videos than PatrickJMT. I can actually understand things more clearly

[@madelinerose-m4q]

I was just on one of his videos and halfway through switched to this 😂

[@jaserific]

WOW much better than the teachers at school.. I actually understand it now.

[@masoomgilani2396]

Could you please tell me how to find the turning point in Completing the Square and also the Line of Symmetry! Thanks...

[@caracervenka]

Still helpful in 2019