Quadratic Formula (proof)

[MsComputerMind]

MathMagician....!!!!!

[saleall]

You should go and try to solve one of those all time unsolved mathematical problems!

[jiaju11]

ty

[DThorn619]

I would never have been able to notice that they both were actually similar to each other :o My mind....my mind.

[Tmanski1]

I love hot girls.

[colin28mac]

I enjoyed solving this along with you

[akukak]

@colin28mac no homo right?

[akukak]

@colin28mac no homo right?

[marissaandmarissaful]

THANKS!!!! this has helped me soooo much!!!! :))

[RollTideTyler117]

life saving video



[LaborHours]

Super awesome.

[tangiblephoton]

This guy is Jesus! I love you Mr Khan!

[JBOYZ14]

I find this hard to master bait to

[apwilsa]

Thanks mate you cleared up so many questions for me. Great Work!

[gautamv8]

get on khans level

[GSlice37]

What if i start off with just x^ 2? I can't divide.

[0ElectricWizard]

@GSlice37 You just divide by the X coefficient, which in your example is 1. So you divide by 1 and the number remains unchanged. In other words, you don't need to divide by A when the the number before X^2 is 1.

[timskeezy07]

At 2:45, why did you only work with the coefficient & not the variable of (B over A)x ?

[justanambulance]

3 people's quadratic equations have non-real roots

[ShakkIsLife]

This is beautiful.

[RnRPwN]

If i get an A i'll like this video again.

[BloomBlossom]

I am not a math person but when I saw the end result of that completing the square, I have tears in my eyes and I've never been this excited ever over math!! Thank you Sal!!

[paulceltics]

thanks

[douchbag26]

is he doing this all with a mouse ?!

[MasterXXChief]

@douchbag26 nah pen on screen

[midgeamoo]

I found myself yelling -4AC!!! extremely loud when i noticed where you were going with it xD

[berkshireshows]

Thanks man, I wondered how they came up with that formula... I think everyone should know how it's derived.

[tamdingonpo]

thank you so much for posting this video...great!

[j4she]

Not sure how you managed to get paid for this, but I think it's cool that you manage to let people pay for downloading it! I know of some teachers who might be helped by your videos.

[princefagwad]

sooooooooooooooo simple

[TheFurryFeline]

you rock my socks

[CrosbySucksDicks1]

I learned this in algebra II. This is not hard to do. I just use the quadratic formula to solve the shit I need to rather than doing all of the work.

[roflcopter2225]

nice proof

[ShinyRayquaza]

i love your videos. you can teach math much easier and faster than any of my teachers i had in school until now :D

[ILuvLatias]

thank-you! this helped me so much on my Test!

[moocat11]

i did the same proof by leaving the a on the left and dividing later. it was not the same format but when i plugged in numbers it worked. shows the versatility of math.

[nvidia116]

This Video Helped me soooooo much!

Thanks! DON'T Ever Stop teaching! 

[dajakesta1234]

tyvm genius

[hobomnky]

lmao! i knew you were gona use green, moslty cuz i wanted green =D

[talaamu]

@hobomnky haha exactly the same thing for me. i just knew he was gonna use green, not sure how.

[talaamu]

@hobomnky same thing here >< i knew he was gonna use green somehow, but i have no idea how i knew it.

[OuttaEgypt]

I know I've said this before, but you're like the most awesome person on this planet. For days I've been scratching my head, frowning, pouting, yelling at my notes and monitor, even came close to tears (well, almost came close to thinking I was gonna cry) because I really wanted to understand the concept behind the quadratic formula and it just didn't register in my puny little brain. By 7:03 my heart raced and I got this stupid grin on my face because...I FINALLY GET IT!

Bless you Sal.

[alitou001]

I think something is wrong in 4:16 when adding the two factors the denominator has to be 4.A^3 (A cube,not squared) ,and the numerator has to be -4.A^2.C+B (not -4AC)...Someone corects me if I am wrong

[enienileg]

@alitou001 you're wrong. later when you square root both sides. 4A^3 would not end up being 2A. the denominator has to be 2A

[Roids1991]

@alitou001 No bro you dont always have to multiply them together to get a common denominator. If you have 1/3 + 1/6, you dont have to multiply 6 and 3 to get a common denominator, you just have to multiply the 1/3 by 2/2 so the denominator would = 6. I hope I answered your question.

[josenros]

Woohoo! Now I see why it works!

[MrJayblaze23]

Nice!!

[solidcancer]

"I hope you found that vaguely interesting..." I found it extremely helpful as well as interesting, needed it for a question set by school. Found the same solution on Google, but having someone talk you through it helped me understand everything step by step. THANKS A MILLION!!!

[oexnorth]

This video seriously made me chub a little bit. I tried proving the quadratic equation before but I had it set up all wrong. Thank you for this, it was fantastic. I'm sending this to facebook.

[MidnightSundowns]

I get it fully until the 2:00 minute mark, ugh I really wish I were smarter in math. I know (like all algebra students) easily how to use the formulas, however I get genuinely interested in the axioms that the proofs come from, but it appears that my brain is not built to understand this and never will. Thank you for posting the video nonetheless.

[ninjajesus81]

That was like magic.

[SpoiledLogic]

great easy to follow proof of something we usually just try to memorize...but we can see that you never have to memorize anything in math!!

[MarvelsofaLifetime]

Lol as soon as I seen all of this starting to turn into the quadratic equation I was beginning to get turned on. I was just like “Oh wow, there it is lol”.

[MasterThief1324]

Solves for "x"

[wavey61]

i kinda got lost at the completing the square thing, but the rest is kinda cool!

[Fishy1021]

hey umm well i mean i was really getting the yellow part at first and then wen it came to the orange and red part it got confusing...can u show more work?? thanx :D or maybe u can help me how did u get the b over 2a squared?

[oexnorth]

@Fishy1021 Do you get the orange part at the bottom? Well, the only way you can get the yellow part (thanks to khanacadamy for color coding this), to look like that orange part so you can break it down into (x+a)^2, is to add some term to both sides, which is completely legal since you are not necessarilly changing the equation (subtract one term from one side from the other and they will cancel). It's a beautiful trick, and it helps a lot.

[C3P0meetsData]

Does this in any way have some connection with Kinnematic equations in physics? (I can't spell)

[oexnorth]

@C3P0meetsData No, you can derive all kinematic equations without ever using this. If you want proof, just ask me, I can do it for you. It's actually quite simple when you see them worked out.

[84sprinter]

This was intimidating at first but I went over the equation and watched the video a second time and I understand. :3 Teehee.

[djnechodom]

Nicely done. Now I can post a link to your proof, since you essentially said what I was said in class this morning (although you used nicer looking colors than I did!).

[Archamber560]

the last part was so touching *sobb*, thx btw 5/5

[EvanYM]

thanks =v)

[guerchr]

this is some good stuff

[Mejiera12]

cool never thought about it that way. great video.

[22admire]

thanks!

[idster7]

i do not get what he is saying from 5:58 to 6:23. someone explain, please? what determines whether there is a +/- provision?

[cherryberrie]

Because every positive number x has two square roots. One of them is , positive square root of x, which is positive, and the other , negative square root of x, which is negative.

[dadwa12]

It is part of the equation when it is put into a square root. You get two answer, one positive, and one negative. However, instead of writing out two problems they just put +/- . This is why the quadratic formula is written: x = -b +/- the square root of ... b squared - 4ac divided by 2a. Hope that this helped.

[oexnorth]

@dadwa12 Yup, you can view it as factoring out the whole square root mess. You know what you're talking about.

[idster7]

i could've sworn i heard the rocky theme during the last minute of this presentation.

[TorasBulba]

THX man u helped me a lot!

[ThelemicLaboratory]

that was great ^THX!

[DeflocculatedDentist]

The end of this was fun

[protosis100]

oye gracias . yo no tenia idea para que me servia la tecnica de acompletar cuadrados y mira aqui lo tengo. gracias me ayudo a saber de donde salia la formula de la ecuacion cuadratica

[DeflocculatedDentist]

math doesn't have a sexual orientation

:p

[DeflocculatedDentist]

Is being gay a bad thing or something? Do you really have nothing better to do right now?

[DeflocculatedDentist]

But WHY is gay an insult where you come from? I'm not gay, but so what if I was? I don't see how some people preferring the same sex detriments you in any way. Stop trolling and go outside or something. It's hard for me to imagine that people like this on the internet actually exist somewhere...

[idster7]

@DeflocculatedDentist actually, math is bi. it screws everyone.

[Penndennis]

@idster7

Hi,

minus x minus = plus.

plus x plus = plus.

ex. -4 x -4 = +16 and +4 x +4 = +16

If x squared = 16 then x could be -4 or +4

Therefore, x equals plus or minus the square root of 16

Hope this helps. Regards, PD

[htkvngr]

This is a fantastic video! Thank you so much for posting it, it really helped me with my maths homework. :D

[duyu]

Thanks!

[myselfable1]

Brilliant, as usual.

[ZaaaHuuu]

Thank you very much for posting this video

[TheRealBravie]

Thanks for the lecture, I liked it!

[AnimeMangaKing]

after seeing ur videos i feel a lot smarter 10 to 100 mins then 1-100 days worth maths teaching in school......thank you

[clemdaughter]

but why do you have to divide everything by A? everyone says they just like to or you should but why? why do you have to have a leading coefficient of one? can it work if i don't divide everything by A in the beginning?

[jorgio375]

The purpose of the quadratic formula is to find the value of x that makes y=0 for any values of a, b, and c.

[DarkReignie]

To derive the quadratic formula from ax^2 + bx + c it is necessary to complete the square, and this becomes a whole lot easier when you're talking simply (x + y)^2. Imagine trying to factorise 947x^2 + bx = -c into a perfect square man. You would fry your brain, so why not simply divide by 947, making your work roughly 947 times easier.

[clallovi]

cause if you dont divide everything by t=ine same term you alter the equation..

its like saying.. 4x+2= 8.. you know 4 has a half..

so what would you have if you divided only 4 by 2 would be.. 2x+2= 8..

which would change dramatically the answer leaving x= 3... what you can do i s divide all terms by 2 which would be 2x+1=4.---> x=3/2

comparing to our original formula: 4x+2=8 ---> x=3/2

[marcusjhung]

I feel more educated from watching one video of yours than sitting through a whole week in my math class.

[LuisF201]

Excelent Sal! you made the proof very easy, when my teacher made this proof, I think he didn't know what he was doing

Greetings from México

[mechwarreir2]

Is there a formula for cubic equations or 3rd degree polynomials? Dare i say 4th degree O_O

[jorgio375]

Yes. They are nightmares. The fourth is just terrible.

[mechwarreir2]

I'd like to see the cubic and quartic formula (by the way, quartic is 4th degree).

[CuberChris]

interesting - i always wondered how to derive the quadratic formula

[tagginos]

Math is beautiful. Thank you.

[trujro0119]

Thank you, i always been wondering how we got the quadratic formula

[Stupifiedman]

You are a math God

[enoughtimeto69]

AMAZING VID! .... ah i feel like such a nerd, i actually got excited when i saw how u did the last couple of steps haha

[nilesgirl95]

thank you thank you thank you!!! i will now pass my math test becuase of this!!!! thank you!!!

[kriskkramer]

I'm going back to school after 20 years to teach math and LOVED this video. Your use of colors was perfect.

[Eeedzy]

you are the frekin BEST, i SWEAR.

[23davidbeckham07]

umm interesting!!

i didnt get the steps right but interesting!!...

[nejtilsvampe]

thx a lot ;)

[Winsunn307]

Thanks for taking the time to do this. It really helps.

[hacksign000]

nice and all but...one thing..please dont speak too fast o.o

[Killap101]

somewhat got lost when u were algebraing but got the gist of it

[xNikic]

gud explanation but i jus dont get it ..

i got the yello i got the orange but ?red?

i dnt get y u did tht

[majorkeybaree]

got lost on the pink,

think ill be watchin this a few times

[GreenCures]

bravo

i need a brain transplant . . .

[Snakez19]

Could have name the Properties you used in each step.

Great Vids, Thanks.

[peroxideh2o2]

awesome!

[viewerlikeyouare]

Wow, you really helped me to understand this.

THANK YOU.

[hipbas]

Hey Presto !!! Like magic. Well done

[stanurban319]

very interesting thanks well done

[demon424]

Fair play, i had no clue what you was talking about .. but fair play you know your stuff

and i watched it all the way through, ya managed to keep me interested even though i have no clue what it was about :D

[initialg]

One of the best videos of seen thus far.

[initialg]

I've*))

[GoldAK47]

By the way, very intuitive vid :)

[GoldAK47]

The only way you can solve cubic functions is by doing Algebraic long division and stuff right?

[Waranle]

Plz can you post more completing the square questions, (like X^3+5x+89), not the perfect square, the odd ones. Thank you

[shiv86]

nice