Completing the Square Made Easy (Precalculus - College Algebra 19)

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How to Complete the Square for a quadratic function and HOW it works.

[@kingtune6836]

Thanks Very Much, Professor, you made me pass engineering mathematics back in college, I'm now a proud electrical Engineer from Kenya

[@trevd2087]

Good job man! He helped me through engineering school back in 2016 as well!😁😁

[@ProfessorLeonard]

Great job!!!

[@iam_mausam]

hey nice to hear, can you please tell me in which field you are working now, and how a day in life look like as an engineer?

[@Alexander-__-]

I’m a student in calc 3 currently at university, and I have to say, I have never completely understood completing the square(much to my detriment) until now. Thank you so much for this video, it has helped tremendously in my understanding of why completing the square works

[@ProfessorLeonard]

I am SOOO glad to hear that. I've felt recently that people might not be getting much out of these videos. It's very encouraging to get this feedback from you. Thanks!

[@wachowski9525]

@@ProfessorLeonard I just came across your videos and I'm blown away at how knowledgable you are and how capable you are proficiently teaching . You 100% are making an impact in this world.

[@rayniac211]

Uni student here as well. I don't even remember if I was ever taught to complete the square. It's just kind of assumed here that I know how to factor any polynomial...

[@meat137]

@@wachowski9525 Yes, he's absolutely the best!

[@thomasjefferson6225]

@@ProfessorLeonard I'm in complex calculus and here. Def helpful. Please do pdes if you can!!!

[@riddlewrong]

36:45 He says to take the square root of both sides, but the square root of (x-1)^2 is x-1. He wrote x+1. It ends up creating a sign error in the final answer of that problem. Other than that little hiccup, this video was perfect. I'm in pre-calc and trig in university and math is very, very difficult for me. I also have a lot of knowledge gaps and things that I've just forgotten from previous algebra classes. These videos are saving my life, really. I don't mean any offense toward my professors, but they just don't teach this stuff in a way that I can understand. Professor Leonard does.

[@tomasdavid26]

Thank you, I was trying to see if that’s a mistake or I missed something that made it x+1

[@dirtyharbor4844]

When no one was here for us, this guy was. Respect 🖤

[@michaelsannella]

self studying math. going back to college after not being in school for 6 years. these videos help me a lot. thank you professor leonard

[@ProfessorLeonard]

MISTAKE... OOPS! As Francis Lim pointed out, at 36:50, there is a small sign error. My apologies.

[@bear532]

You fail. Zero for you. All joking aside, thank you for the videos.

[@PaKiKiNg908]

Thank you so much Professor Leonard! You are making Calculus fun for me!!!!!! You are a blessing to Mankind! Thank you Sir

[@GoatzAreEpic]

@@bear532 bro that's not cool everyone can make mistakes. Admitting your mistakes and improving them is what makes us grow as people!

[@ANHPHAN-bi1pc]

went to go ask my wife if the professor was right on this sign! was going crazy for a sec lol

[@hahahahahahhahaha6]

@@GoatzAreEpic r u slow...

[@saikumar-xh9vc]

professor i have gone through your's all cal1,2and3 videosafter my four years of degree in B.E now i feel i am comfortable with calculus , your service to world of math learners is fabulous . sir please continue your service and thanks a lot from INDIA

[@ericsills6484]

I love how you say we're learning this here because we'll be using it later down the road. Back in the day, my teachers didn't want us to worry about what was ahead. It would've been helpful to me.

[@NYCGemini2000]

I’m taking precalculus now and I bombed my first exam. we have 5 exams left and 2 finals. I refuse to fail this class. I’ll be watching videos on KZbin all day

[@notreyreyes]

I got an 82 on my calc exam thanks to Prof. Leonard :))

[@onemanenclave]

82? that's not 100

[@bigshaqsmathematicalinstit3318]

Fled From Nowhere Please don’t hate! There is nothing wrong with getting a B, good job on that 82!

[@ProfessorLeonard]

Good job!

[@dunemae]

@@onemanenclave You don't know their starting point, it could have been much lower than that. Be kind to people.

[@nicoleodonnell6287]

Thank you Professor Leonard. I became a math tutor recently, and your videos are so good for reviewing/knowing how to explain things in a way that is easy for students to understand. And I also direct a lot of students to watch your videos when they need more instructions. Especially the ones taking online classes will tell me that your videos are really helpful. I watched them a lot when I was taking precalculus and calculus online too, and they helped me so much.

[@georgesadler7830]

Professor Leonard, thank you for Completing the Square Made Easy in Precalculus and College Algebra. The examples/problems are outstanding, and students should take notes and practice for a deep understanding of the material. The Organic Chemistry Tutor and Professor Leonard are number one and two on KZbin.

[@kelvinlikollari1576]

Ι passed my Calculus with a 8 mostly thanks to you. God bless you!!!

[@shantyman.]

i understand everything !!thanks prof for teaching , your the best

[@kater6873]

Thank you so much, Professor Leonard! :) You made me learn to love math and have changed my life for the better!

[@deeperthanseen5664]

I didn't know this was for undergrads and I've been watching these videos for months...We have this in our class 10 portions in India...Thanks a lot professor!! I was confused in a LOT of things but the teachers simply rell you re read the textbooks and memorise the formulaes.

[@sandileyaze2380]

Thank you, Professor Leonard, you've enlightened me.

[@georgettebeulah4427]

This is so much meaning and making much sense and can relate to it a lot.

[@richardsummitt9295]

I really appreciate the fact that you explain why we use completing the square, and why it works. Thanks! Hopefully this helps me on my exam on Friday!

[@Eudaimonia7564]

Did it?

[@richardsummitt9295]

@@Eudaimonia7564 it did! Ended up getting a 93% currently have a 90% in the class!

[@hickelpickle]

Here I am studying algebra for calculus, on the same exact topic atm. Taking a lazy break and checking my youtube subs, as the wall of text explaining it is intimidating. And this video pops up. TY, got a feeling I'm gonna really need this video.

[@franciseylim11]

Been waiting for few weeks, finally. Your new video really makes my day, thanks. 😉

[@petermurphy9330]

You are the man, my mathematical inspirational. As somebody who has ambitions of teaching High School maths, you are pointing the way in detail!! Your explanations make plain the complexity and majestry of mathematics, providing a pathway for all to follow. More power to you sir.

[@waleedmuhammad1484]

He knew we would be having this prob during calc 2, best teacher ever !

[@crispinkawana2750]

Prof. You're an awesome, lovable teacher. Teacher of teachers.

[@theoremus]

Thank you Prof. Leonard for explaining.

[@theoremus]

Prof. Leonard, May I contact you about my work on the quadrature of ordinary curves?

[@paulmaggiar8274]

Thank you, Professor Leonard. Actually, the last example, at 1:00:20 has no x intercepts as can be verified on a graphing calculator.

[@zyleaf]

Thank you for always improving your methods and making it easier for us! The diamond wasn't this developed when I learned to complete the square from the intermediate algebra playlist. Now I can use the diamond method to complete the square too!

[@almafabiolasoriacontreras9445]

You are math life saver =D. I hope you get back soon! Thanks for this legacy!

[@isaacwolford]

Thank you so much for this video! Without this type of teaching that really explains stuff... its no wonder why people hate math so much! Keep up the good work! :)

[@thapelomaja8333]

Thanks Professor Leonard Too much respect 🙏💯

[@Kaaxx123]

your lectures are really understandable for nonnative speakers of english (sometimes i had to rewind some of the videos) but im already few years ago my school time

[@wanyangqiao9829]

Thanks for teaching this convenient method, I am now full understand.

[@busrraengin]

Thank you for the explanation Professor Leonard, it was super helpfull.

[@rayj1232]

HES BACK!!!!!

[@ProtoMaxoid]

A nice review. Thank you Professor

[@introvertedengineer2937]

Prof. Leonard, your videos are nothing but helpful, fun, and informative. Thank you so much for all you do to help us students and making math awesome. Thought: I think if the term was called "Creating a Square" rather than "Completing the Square," there would be less confusion.

[@NadiaFGreene]

Love how enthusiastic you are! Thank you, this did help. Could you, please, post another video with a leading coefficient > 1? I'm doing khan academy, which has that, and I'm just not getting it at all

[@abelwolf7141]

Mistake Alert: @36:47 its x-1 , the professor accidentally wrote x+1 --- Thank you Prof Leonard!!

[@thangarajselvamani178]

Thank you , Sir.

[@dragmahk]

Am I the only one who thinks the algorithm he teached on Intermediate Algebra is easier/less prone to error? I mean this one: -> Write as ax^2+bx+c=0 -> Isolate variables on one side, constants on the other -> If "a" is not 1, make it 1 -> Take half of "b", square it, and add it to both sides -> Factor the perfect square trinomial -> Solve.

[@crispinkawana2750]

I am loving it!

[@Andy-jt5sr]

Professor Leonard,I found a mistake at 36.57: it has to be x-1=+-squareroot of 3/5. Thank you for your work,much love!

[@maximoleon5295]

huge thank you

[@pankhuriagarwal2772]

Professor .. if possible , can you please start trigonometry and give a break to algebra and continue it later , because we can find algebra in intermediate lectures also .. And Thank you for your efforts ❤️

[@Himawari_.]

Professor Leonard, thank you for providing us with very awesome explanation about every subject. I appreciate it so much. May God bless you for your kindness. Professor, I have a request. Can you make a lesson about Mechanics as well? Thank you Professor.

[@green_quadrix]

Thank you 😌☺️

[@yehah]

Thank you for the video Professor Leonard and happy 2022. Out of curiosity, do you have examples on how to integrate by completing the square in one of your calculus videos? Thank you

[@ankitchakraborty1126]

Hi, @Professor Leonard; thanks a lot for making this incredible series. I am 29 and who studied Physics. But it is now that I am genuinely enjoying and understanding maths. P.S.: I think there is no X-intercept for the last question, as I have an imaginary solution. Can anyone kindly verify whether I am right?

[@manishpingale6558]

Great video!

[@vishalmishra408]

@professor Leonard. There is a writing mistake in this video ( video #19 completing the square made easy) at 36:45 minute you wrote (x-1)^2 and at 36:49 minute (x+1). That completed changed your solution at 37:15 minute.

[@BONTUTESFAYE-g5b]

you're genus

[@jenrim]

That last quadratic equation doesn't have any real roots. The discriminant is < 0, it's -31. I checked by entering the equation in Grapher and it confirmed that there are no x-intercepts.

[@chocolateangel8743]

When you Complete The Square, "A" does NOT have to be 1 (if you use the multiplicative property of equality). I also find that this makes more sense with an area model. If you have the time, you should check out the Quadrus Method by Dr. James Tanton.

[@daliggy4503]

Why not divide the whole problem by the number in front of (a) instead of factoring. It seems easier and you don't have the possibility of error from missing the distribution.

[@wildchild1161]

I am currently in diff q , I Always forget how to do this , dunno why but i am just like Uh how does this go again . Been waiting for this one for a long time . Thanks Maybe now i wont have an excuse for forgetting it :p

[@wildchild1161]

and im back cause i forgot it again lmao .

[@maksymandrzejdrzyzgiewicz5096]

@@wildchild1161 lmao

[@cw4933]

lifesaver

[@JA-om2ze]

I love you!

[@adantephil8833]

@36:46 how does sq. rt (x-1)^2 become (x+1) at 36:52? It should have remained (x-1). Am baffled. Any one to clarify this?

[@dunemae]

He corrected himself in the comments. A little late but just for anyone else who's confused.

[@austinboji9327]

I wish you would do similar triangles next

[@slr150]

1:00:21 No real x intercepts for h(x) the solutions I got were: I got 5/4 + √(31)i/4 and 5/4 - √(31)i/4.

[@Jackson-tb1jy]

Hey Prof. Leonard! I know it's been a while since this video was made but wouldn't the very last problem result in imaginary numbers?

[@davidvolland7250]

That’s what I came up with a parabola that opens down with vertex below the x axis check on a calculator

[@miskhar]

I was curious....it seems like the final example actually has a complex solution. So it seems that this parabola would miss the X-Axis entirely, right?

[@stephenhemingway9435]

@36:51 you write x + 1 on the LHS. I believe it should be x - 1.

[@jogedomato2765]

The Good Lord bless you professor Leonard

[@ecokecok1376]

Hey professor I calculated the last functions x-Int and they are Complex. The intercepts are x1 = (5+2i(31)^(1/2)) / 4 and (5-2i...) / 4

[@nobeltardis1930]

Thank you so much, your videos are very helpful. We are waiting for more videos from you professor!

[@nate6199]

Do you know how many more videos will be in the college algebra section of this course?

[@ridh7125]

Hello professor, just wanted to ask, at 36:53 , wouldn't it be (x - 1) = +-sqrt(3/5)? instead of x + 1 on the left of the equation

[@allahuakbar9884]

i want to trust in my math ability as much as this man trusts his skin to hold in his biceps in

[@xinsane7619]

legend :)

[@ElegantAstronaut]

Hi professor, when I solve any equation that contains fractions I convert them into (0.), the final results I’ve got is -0.92 and 0.32… is that considered as a right answer? Thanks!

[@franciseylim11]

I’m so sorry Mr. Leonard, at 36:50, after (x-1)² = 3/5, you wrote (x+1), it should be (x-1) right? Just double check, don’t worry.

[@ProfessorLeonard]

OH NO! You're very right. Thanks for the follow up!

[@SonuSingh-qw2bs]

Hello professor i have a question? x^2 + x - 1 how to find the x intercept please if you can explain me a little bit and how to graph this one because i'm getting some too much things and the book points are not mentioned

[@MathForAll81]

There’s a typo at min 37, (x-1)^2 =3/5, then x+1 = sqrt(3/5) …. It supposed to be x-1 = sqrt(3/5)

[@hottwheels83]

Is your "add and subtract" from the same side, in order to put the equation into vertex form?

[@IMadeOfClay]

Hello Professor :)

[@andrewgarcia3967]

kzbin.info/www/bejne/qonVqpSDYtKHprs If you go to this link at 1:27:55 (1 hour 27 minutes and 55 seconds), you will see that he uses a partial to connect "X" to "U". But at the beginning of the video he says that if there is only one independent variable we are connecting the intermediate variable by normal differentiation(dx/du) NOT PARTIALS. So my question is why does he use a partial in this case? Also, the problem is: w=xarctan(yz) x=u^(1/2) y=e^(-2v) z=vcos(u) FIND δw/δu and δw/δv​ Please explain the part where he connects X to U by using a partial. How can he do this if there is only one variable we can respect too in terms of x(u). IT MAKES NO SENSE to use a partial when you can only get a normal derivative x'(u) NOT partial X with respect to U.

[@acercomputer6714]

hi. I didnt take 5 out from (5x^2-10x). I said I have to add 25 because to obtain -10 , x should be equal to -5. -5*-5=25. Now I have 25+2 = 27. 5x^2 -10 +25 +2 = -25. (5x-5)^2=-27. As you see here I got wrong answer.

[@The_Angry_BeEconomist]

I should have watched these before doing the calculus videos

[@ahmedmohamed-yx1ln]

💓💓💓💋💋💋 I love you from egypt

[@shaggy6249]

can someone explain why Professor Leonard turned the denominator from 4 to 2 at 26:00 Im looking at desmos and the function graph does not match with x=-3/2 +- sqrt5/2 however it works with x=-3/2 +- sqrt5/4 so the change from 4 to 2 confuses me

[@glorykaur5868]

the square root of 4 is 2, he just simplified it. as you would for example if you had a sqrt9, you can and would write it as 3

[@ecarat972]

How did you get the number 3 I am so confused?

[@jogedomato2765]

...with many years of life making new friends

[@srivatsraju972]

at 1:00:34, isn't the solution imaginary?

[@deluca4750]

I was scanning the comments looking for someone to mention this because I ended up having to take the square root of -31/16. Plugging the equation into Wolfram Alpha also ends with imaginary solutions.

[@gregg8010]

Houston, we have a problem. That last quadratic has no Real x-intercepts.

[@dianeyoung8130]

yep

[@Clutcch]

19

[@NobSwitch]

You should be getting my tuition, not my professor that can't be half-assed to explain anything.

[@mia.martin8]

There's also a mistake at 58:48. There has to be -25/8 so after distributing it'll be -81/8

[@guidofeliz8384]

You made an error in your work for h(x) = 5x^2 - 10x + 2.

[@phol5082]

38:44

[@ColinDowney-zt2tt]

36:00

[@benhbr]

As much as you empathize with your students struggles and guide them along, your lectures could profit greatly from more visuals. They would add a lot of insight into the symbolic methods. For example, in this lecture entitled ‚Completing the square‘, you never draw an actual square.

[@roadtoad3484]

I really enjoy your videos but I miss the interactions you have with students in your classroom sometimes you make me laugh and these videos are lacking that. Is there a reason why you dont have in class videos?

[@ProfessorLeonard]

They stopped letting me film in front of the students. It's sad, but it's true. There are benefits to this though... less distraction and more time to spend explaining when necessary. I hope you can still get as much out of them :)

[@floortrader60]

did anybody else get x = (5 + i (31^.5))/4 and x = (5 - i (31^.5))/4 . I double checked, I will triple check

[@peterpalumbo1963]

You probably should have drawn the graphs too.

[@rickhoro]

I'm not the first person to notice this, but I believe the last problem has no real solutions. sqrt(-31/16) by my calculations.

[@Devayearsago]

idk why it feels illegal to add a new number to an expression lol

[@JC-si4db]

This dude starting to look like Henry cavil

[@ultimate09ozultimate09oz]

Oh god i don’t get it. I should rewatch the video some time again to grasp it.

[@guidofeliz8384]

Why not write steps on the board for your video lessons? You do that in your class videos but not when talking to an empty classroom. Why?