Completing the Square - Solving Quadratic Equations

[FinishingCircles]

thank you lover. first thing i've found that actually explains what to do with that +9 and -9 <3

[singhsangha]

Awesome, dude!

[MobileTurd]

this is great. thanks a lot

[Jaytheozzi]

i found this was exactly the same equation i was looking to understand out of the text book....

[MrCHeRFY]

I could fall asleep to your voice.

[ilikecheese1786]

YOU ARE AMAZING

[biolexyable]

thanks brah at first it was like a magic but know it makes so much sense thanks a lot...

[bando26]

Something nice about seeing the equation in the form (x - 3)² - 1 = 0 is that you can see the global minimum. The squared quantity is never less than zero (it is zero at x = 3); then, there is the -1 term there, so the global minimum is -1.

[blackandwhiteangel13]

Omg it make sense!

[gangsterelmoman]

Haha you make it so much easier than my teacher dot kelly

[connorcougar]

wow-studying for 1 1/2 no results- 4 min video i get it now thanks!!!

[NightClash909]

There are no extraneous solutions for this right?

[Moongazer980]

I was sitting in class taking notes and askin questions for an hour and a half...didn't get it.

Watch 4 minute vid....now i get it XD

[deeppurple28]

Thank you Patrick, you have helped me A LOT!

[chelseafcfanisy]

patrickJMT, you are by far the best human being on this planet. God Bless.

[xXF1eeXx]

I'm in 8th grade and im barley learning this stuff

[c0rrupt3dlyfe]

i wish i had watched this before going to school to take a test this morning....

[dialectical44]

What is the signficance of subtracting the 9 from the 8?

[beckyelliott3]

@dialectical44

You are adding 9 therefore you also need to subtract it (this is because you can't arbitrarily add in a number to an equation without changing the original equation. By also subtracting it you are keeping the original equation.) You subtract it from the 8 because we put that number outside the parenthesis, therefore we add it to the inside but subract it from the outside and ultimately keep the equation the same.

[zelaileeds]

I love u

[NoGutsNoGloryLEAFS]

When he had (x-3)(x-3), can someone please explain why the roots were not simply +/- 3?

Grade 10 academic math is my knowledge

[aalvari1]

You have a gift with mathematics and my savior for reviewing old material I have now forgotten

[navyalex434]

how did you get rid of the Sq.root on the 1 and come to the conclusion that x-3=+/1-1? I thought it would look more like x-3=+/-Sq.root of 1 since you can't just get rid of the Sq.root of 1. Anyone who can help is welcome to. Thank you!

[Adamgoldminer]

@navyalex434 The square root of 1 equals 1.

[far0ashgar]

Thanks for sharing.

[NazzMaximillion]

he's fucking brilliant... i was lost and now i'm found

[yisoonshin12]

MY GRADE WENT FROM B TO A NO JOKEEE seriously in my class apparently only 3 people got A's last year so I'm happy I'm hoping to keep it up :)

[WebbTunes]

Thank you!

[Campeonesaguilas]

Dud thankyou so much my grade in advance algebra went from a C to a B now that i watch helpful videos

[Tennismaster97]

Wow ur better than my pre-calc teacher... Thanks A lot

[sonnytenedo]

Mom asked me If I should take tutoring in my school... I said with a serious face "The internet teaches better than my teacher"

[Raindropp11]

super helpful!!

[krisjanhortal]

What if the factors we derive is not a perfect a square?

[ladicius]

good move.

[gravyhouse]

I wish I had looked for these videos two years ago

[EsmayMaria]

Thank you! You saved me from a full lunch break of detention! :D

[manahara8]

@squalestang92 exact same with me! thanks alot Patrick :)

[slamshrk31]

you're handwriting is so good

[Squalestang92]

Im currently taking a calc course in college and I had to recall how to do this, this did an excellant job in teaching it and refreshing my memory...thanks!

[eco512]

What if that -3 was a positive 3 would it still be a positive 9?

[BabyILikeItx3]

@eco512 Yeah, because a positive 3 times a positive 3 is still positive 9.

[matprithellodave]

@eco512 yes.

[Carolinafilms95]

I've been trying to understand this for 2 weeks, gone through loads of other webpages and books my teacher has told me to go through and yet i still couldn't get it. I watch this one video and now i know it like the back of my hand. Thanks!

[Drspankie]

OMG thx so much man you saved my ass from failing

[XIIxMysticxIIX]

thank you!!! I'm finally gonna start doing my homework this semester...hehehe

[kidhbailey09]

ahh! I swear these youtube video's is very helpful when needed and as for my teacher..... ummm your getting there once it comes to explain the problems/answers. lol!

[nanc33mc]

you are a good teacher :)

[plasmadragon1998]

@nanc33mc You are the best math teacher Ive seen!

[FiniteStar]

thanks it's super understandable.

[kallewade]

Pre watching vid: It used to take me about 10 minutes to do each problem and I did not always end up with the right answer After watching vid: Your way has cut my time in half and I have the right answer. Thank you!

[boredagain1]

Why do you always take 1/2 of the coefficient in front of x?

[ILikeReallyBigButts]

@boredagain1 Procedure. 

[colts0082]

haha yeah you saw right through me... chapter quiz tomorrow :(

[Strife18]

THANK YOU! My college teacher was discussing this Monday and I couldn't understand what the hell she was talking about. You explain it so much easier. Now I can finally get my homework done!

[kaspersky2020]

thank uuuuuuuu so much

[UltimateCybress]

VEry helpful. Thank you

[Guineapig300n60]

Thanks man, video really helped!

[JSunJShineR1]

Was going to watch this video before my quiz I just took but only got halfway through and whadda ya know? complete the square showed up and I only knew how to do it halfway through, at least I'll get partial credit. =P

[mariolaaaa]

thanks for teaching me things that 1.5 years of pre-calc (and 2 shitty teachers & TA's) couldn't teach me

[thepieface9496]

thanks this is really helpful

just a tip dont write the x's like multiplication signs its confusing like that

[thepieface9496]

thanks this is really helpful

just a tip dont write the x's like multiplication signs its confusing like that

[thepieface9496]

thanks this is really helpful

just a tip dont write the x's like multiplication signs its confusing like that

[PHATSTR]

I dont get it!!!

[Chris40679]

Why couldnt my teacher be this guy?

[sweata71]

what do you do if on the rights its -1? You cant square a negative unless you want to work with imaginaries.

[rebeccasung95]

Left handers ftw.

[GanzuGinisu]

OMG! thanks! this is a better explanation!

[KrinkKut]

Thank you so much for all of your help man! I really appreciate it.

[thegiant1994]

Hey good job, I am starting A levels and your video helps me refresh my memory on this topic even though I got top marks for my GCSE, summer holidays really make your skills go all rusty. xD

[Fledge2010]

Thank you so much for uploading this! It made my homework so much more understandable.

[toupitilili]

thanks patrick :)))

[ezawarr]

thank you i couldnt get this i tried everything and this is the only ting that worked :)

[Mgamerz]

GREAT tutorial. Really helped me remember how to do this for my calc 2. Thanks!!!

[KosukeBlueDragon]

What if b=3 1/2(3) =?^2 will it remain fraction?

[MOMMYLUVSLEXIE012109]

Yo Patrick, thanks a lot for this video. It really did clarify all the questions that puzzled me about the process of completing the square.

p.s. this is the first comment I have ever posted in my history of watching utube vids. so I really do appreciate the instructions you give.

[bakedoughful]

lol.. all the comments have so many likes ;)

[x3Em0zz]

i love you

[TheCj700]

I can't believe how much my teachers missed out in this topic!

Thank you sooo much for explaing this!! =D

[L1tezpeed]

Wow you have such nice writing!

[Therealkrazy06]

Who else googled "how to complete the square"?

[HCFMB]

how did you get the 1/2?

[rodmaitim]

You rock dude!! I think i can save my almost-failing grade in college algebra today!!

[reid13096]

i wish you were my teacher...

[E90PAT]

Pat youre a boss

[CeciliaWearsPrada17]

Can you tutor me? Lol

[Noremae]

I know teachers in math are good in math, of course! But some don't teach math as efficient as you are.

[YellowChick51]

57 people failed Math in high school.

[whitenbald]

Thanks :)

[iluv11alot]

I just realized you were a lefty. BEST LEFTY HANDWRITING EVER

[Billionaire851]

Why do I go to math for an hour to TRY and learn this, when you could teach me in five minutes!

[mrwhiskersss]

thanks so much bro, btw I like your handwriting lol

[LIVELOVESHARRY]

stick around if you need to see that example :)

[youngmastermagican]

Thumbs up if you have a test tomorrow!

[Faaaatiiimaaaa]

I love your writing......=D......

[94mbu]

I HAVE TEST TOMORROW >:)

[mu51im]

I dont know why I'm saying this but I just love your red pen lmao

[juicirosi202]

Thank you so much. I have a test tomorrow and without this expaination,i would fail.<33

[122ariana]

thank you! this helped me so much!



[hazdoga9]

i have a test in a few hours, not tomorrow sillly

[organicbeanful]

maths GCSE in 1 hour. I still don't know how to do these but atleast I tried to revise XD

[1blastboy]

math test tomorrow

[iamkenia]

Finals in two days. It seems that I forgot everything I learned this semester.

[infernocombustion]

wow, thanks so much for uploading this

[BatterdSloth]

you ought to win an award for that tick!

[BatterdSloth]

Thats one of the best ticks ive seen in a long time.

[BatterdSloth]

Thats one of the best ticks ive seen in a long time. Oh the simple pleasures...

[Rob1Esco]

i HAVE A TEST TOMORROW!!!

[pandaluver101010]

that is cool that you are left handed



[rayraymar1]

Your my new teacher

[NoTurmoilPlz]

great vid man! still confused about quadratics but this helped quite a bit :)

[Bloomsfreak77]

I think that because there are some people who actually apply themselves to their tasks sometimes even months in advance, that video hunters should not be "labeled" as slackers. I know there are multiple resources and I will use them as much and as often as I can. Have an awesome day and for the instructor of this particular lecture. You are wise, you win some and you lose some, keep doing what you do best because everyday you change someone's life. C=

[sketchmo1]

I love you

[Chronothread]

How on Earth did people give this thumbs down? I'm not saying it's the most amazing video I've ever seen, but it's correct and well made. I don't understand how someone would go so far as to consider this being worth a thumbs down!

[WhutsWhat]

LOL I liked the drawing of the little guy who is actually ''completing the square'' :P

...and by the way, thanks for the video!

[mynamehere8693]

what if you're applying trig. like sin^2(x)-2sin(x)-3=0 and you have to find sin?

[vish0somani]

what is the right side is zero!!?

[vish0somani]

Yeah! fine I have my finals tomorrow. So, thanks! :)

[SongHyoRi]

that little stick man at the beginning completing the square is so cute! ^_^

[OO1VideoVoid1OO]

THANK YOU ! Finally someone who explains it with detail and precision. My math teacher moves too fast for me to even keep up with his notes. Again thnx.

[leezhijiang]

U give me a clearer look

[mtimpy360]

i love you man thank you for the math vids

[PeaceSmileMUSIC]

Helped me so much~ thank you~

[othobsessed2]

you have very nice handwriting.

[cubanita365]

i understand the rest, but where/how did you get that 1/2 at the beginning of the equation when you out it in front of the 6, and why did you put it there? how is 1/2 in front of the x? that is the only part that confused me.

[darandomizer2]

@cubanita365 you add [(b/2)squared] to both sides of the equation. It is just how you solve "completing the square equations".

[caesiume]

I can't believe I just learned how to complete the square in a few minutes. The internet is cool.

[jumanahLOVESrock]

how come you took off the radical for 1 and just made it +- 1 ?

[bomrdude]

I've noticed that people only look up math videos if they have a test the next day.

[patrickJMT]

@bomrdude yes, and then they complain about how nothing makes any sense. i love it.

[GrayFox1203]

@patrickJMT I just think your videos are easier to comprehend and understand just cause you go slower. I Math has just been one of my weaker subjects. What makes it harder is that I have an incredibly dull teacher and I have it 1st hour when I'm really tired and not paying attention anyways. Your vids are nice cause you go at a good pace, I can look at them on my own time, and you don't bore me to tears :-)

[jiamonx2]

@bomrdude funny because ive got a test tmr

[SCCfann]

@bomrdude you think that's bad? I'm supposed to be taking the SATs this weekend. I didn't know I'd have to take them until about 2 and a half weeks ago (long story). Now, I'm sitting here trying to remember what I learned in high school and college math.... Now, I've always loved math, but if you don't work on something continuously you lose it. Yeah.... I've kinda lost it. :P

[patrickJMT]

@SCCfann i never once studied for the ACT and the SAT. just walked in, took 'em, got outta there.

[HamdhanA330]

@bomrdude no, not really, dont have a test but have homework

[standingpretty]

@bomrdude LOL how did you know?

[TropicalLove07]

@bomrdude Not the smartest idea.

[RollTideFootball]

@bomrdude Hey!....yeah your right...i gotta test tomorrow. sigh

[gbuitronccc]

I have a test in two months does that count? :)

[Yelliesbabe19]

@bomrdude that is like so true, that what i do lol..

[magellan46]

@bomrdude , thats the exact thing im doing now!



[AlexNash08]

@bomrdude Guilty.

[thehousefox]

You sir. Have saved my life. And for that I salute you!

[TiNkfAnGc]

that not rit at all u divide each number by 1 cus theyrs always a 1 infront of an x

then after that u re write it again which makes a new eqautions and then u do a build a wall problem whcih gets rid of the o then after that u keep going

ur way is sooo hard to do!!

[patrickJMT]

@TiNkfAnGc i think it is rit

[dooodadooo]

@patrickJMT lol such a bully

[singhisking853]

@patrickJMT So you're trying to find the x-intercepts right?

[UploaderA]

VERY HELPFUL , I HAVE A TEST TOMORROW ! THANK YOU !!

[itwonthappenagain]

My precal teacher never help me this way :( hope I had a teacher like you. Thanks alot ^_^

[STFUuBunTing]

nice

[destructodisk]

howcome all math teachers have sexy ass writing :/

[psunny24ify]

u did it the confusing way

[matthewamac]

@psunny24ify Some questions have to be done in this format.

[frozenyetimaster]

I don't understand why you do it that way, there is a simpler way you can use to solve it with the same method but in only 4 lines...

[matthewamac]

@frozenyetimaster Some questions require it this way.

[frozenyetimaster]

@matthewamac

you can get to the same answer without writing SOOO much crap....

[matthewamac]

@frozenyetimaster You might not have the answer in the same format. Some questions specifically ask for the format to be (ax+b)^2 + c and doing it through other methods are not acceptable.

[frozenyetimaster]

@matthewamac The method I was taught get's you down to (ax+b)^2 + c. Then we are supposed to square root c, so that we could form a difference of squares and then factor it even further.

[bvwest53]

I had questions for my algebra professor on tommorow regarding completing the square as to how he arrived at a third number that was not part of the original problem. I noticeded that he did a b\2=16\2=8 squared, however, he did not explain this notation to us. Thank you for allowing me to exhale with completing the square. I appreciate your thoroughness.!

[bvwest53]

I had questions for my algebra professor on tommorow regarding completing the square as to how he arrived at a third number that was not part of the original problem. I noticeded that he did a b\2=16\2=8 squared, however, he did not explain this notation to us. Thank you for allowing me to exhale with completing the square. I appreciate your thoroughness.

[bvwest53]

I had questions for my algebra professor on tommorow regarding completing the square and he arrived at a third number that was not part of the original problem. He missed that step. Thank you for allowing me to exhale with completing the square. I appreciate your thoroughness.

[diamondkyle15]

I have come to the conclusion that I love you. 

[Surya0905]

superb 1 mr.patrick.....2morrowz ma exam n i apreciate ur video assistance....ver much....

[hellogorgeous15]

im a university student and i had a major mind block and totally forgot how to do this lmao . thanks!

[2SnapOrNot]

This year my math teacher is a bitch so I have learnt nothing from him. HOWEVER these helpful youtube videos have helped me keep on track. Thank you :)

[cambroni28]

Seriously, learned more watching this video once than I did watching my math teacher for 3 day. Thank you!

[kkcrucial99]

this was really helpful thank you

[MsRhonda01]

can u do radical

[LemurMan2008]

i love you

[igugus]

lefty just like me

[NightShadeslayer]

What about completing the square with more than one variable? And I don't mean a circle, I mean:

x^2 + y^2 - 4x - 16 =

[jjb302]

how come you dont (add) nine to the otherside but instead take it away cuz in other videos they do the same thing to both sides???

[frenchfriesidiot]

@jjb302 He didn't add it the 9 right away b/c he is using a different method. It will give you the same results anyways. Try it yourself. First with your method of adding 9 already and try his method of just subtracting right away. It has the same result of a positive 1 on the right side of the equal sign.

[TheXxGreatxXOne]

THANK YOU. EXAM ON MONDAY :(. GR 11 FUNCTIONS, you helped a lot

[patrickJMT]

@TheXxGreatxXOne good luck, and keep studying!

[kakakarlyn]

@TheXxGreatxXOne SAME !

[Xiabuse]

@kakakarlyn fucking same.

[juumdd]

exact same method my teacher taught us

[oronimo]

Thank You!

[ruthampton]

I have a math final tomorrow, and am doing a lot of graphing of quadratic functions. This helped me out a LOT, because I was having problems understanding fundemental math problems (such as completing the square lol). I just wanted to say you're way better at explaining than my current math teacher aha. Thanks!

[icefan11]

this guy is fucking retarded

[devillord18]

Holy cruds! Don't say this is in the higher papers? I'm screwed if it is, there are enough difficult questions I've told to learn... now this... geez

[cacalloway]

PLEASEEE don't listen to the people commenting on this. you're doing an AWESOME job of saving my grade. THANKSS!! = ]