Solving a quadratic equation by factoring | Algebra II | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Practice this lesson yourself on KhanAcademy.org right now:
www.khanacadem...
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
/ channel
Subscribe to Khan Academy: www.youtube.co...

[@laurenbethune2318]

Nope, I still have no clue what's going on

[@ThePussukka]

kzbin.info/www/bejne/jmilkKd-abRgldU this helped me to understand this video

[@vicwang271]

Lauren Bethune are you dumb?

[@laurenbethune2318]

Vic Wang apparently

[@vicwang271]

Lauren Bethune what do you mean apparently

[@laurenbethune2318]

Vic Wang I mean, according to you I must be right, since you think it's so odd that I didn't understand this concept?

[@sevenisacannibal]

guess i'll just die.

[@shoaibkhan-qx3oq]

its been 3 years are you dead

[@omarkhattab5230]

Yeah same

[@sevenisacannibal]

@@shoaibkhan-qx3oq only on the inside.

[@youtubeenjoyer5083]

@@sevenisacannibal still?

[@shawtylikeamonke]

@@youtubeenjoyer5083i am

[@izu1489]

i don't understand my teacher. i don't understand this also. i think it's time to plant in backyard with potatoes.

[@universalyoutuber195]

It’s been 2 years did they grow?

[@hemavathi1028]

@@universalyoutuber195 lmao

[@izu1489]

@@universalyoutuber195 omg idk why I said this HAHHAHAHHA. maybe I'm the potato 😭

[@face112]

Thank you so much! Thanks! In my head, It feels like someone walked insinde a dark room and just turned on the lights.

[@russiangravy3870]

Dork

[@preparator9925]

Its almost poetic

[@sherrydiep839]

@@preparator9925 facts

[@ryanissa3353]

Who else is here for an assignment?

[@ricky_boi64]

Yep

[@abayerr279]

Yessir

[@kaihaughey4008]

Mhm

[@AafiyahMahomed]

yes unfortunately.......... :(

[@GetUpAndWatchVideos]

Instructions not clear enough. Got my slong stuck in a toaster

[@Bee23447]

My personal recommendation to fixing your problem, Slong = Toaster

[@TheWiery322]

im completely lost i have no idea whats happening

[@vardag3196]

I'm a little late but basically you take the product of the first and last terms and find their factors. Then you chose factors that when added or subtracted equal to the middle term. Then you make pairs of two and then take out commons and the stuff in both brackets should be the same. Then you delete one of the brackets and then put the stuff outside the brackets together into a bracket and your done. I suggest watching some more videos as I am absolute garbage at explaining things

[@TheWiery322]

@@vardag3196 wow thanks man, definitely haven't dropped out of college since this comment was made. Definitely a relevant comment to make. Big ups friend.

[@vardag3196]

@@TheWiery322 I don't know if that was sarcastic or not. If it wasn't your welcome. If it is, dude I just got in grade 9 and I am just starting to learn this. You should never have dropped out of college. Stop being salty at a minor who was trying to help you yet you are taking out your anger at him.

[@TheWiery322]

@@vardag3196 bro I wasn't mad. It was complete sarcasm. Sorry if it came across wrong. And I did'nt know you were a minor. My apologies

[@nniiania]

How to solve mathematics: Step 1: Write the equation Step 2: Cry your eyes out

[@Wentrashane]

Exactly

[@Goosiepoo]

Yep

[@insaneshadow85]

It took me a few days, but I think I'm starting to get this. I can't wait to pass the math part of my GED, it's the only subject holding me back.

[@martinc8325]

About to try and get my GED, really scared of the math portion

[@davidk1308]

insaneshadow85 Same here! I'm terrified!! D:

[@itsbk6192]

So Did you?

[@Goosiepoo]

We need to know

[@universalyoutuber195]

Did you do it?

[@onedgivesmelife5741]

YOU MADE IT SO COMPLICATED IT WAS SUPPOSED TO BE REAL SIMPLE

[@vicwang271]

yna how????

[@david.ricardo]

Because he really wants you to understand math not just solve equation without knowing what you are doing like a robot

[@evie5375]

@@david.ricardo fair enough but i just wanna pass

[@enixepyx9001]

@@david.ricardo chillllllllll mate

[@omaralkindi1315]

@@david.ricardo You never know if that's the case, dude can possibly be the next bill gates. Don't go judging people around for what their not good at.

[@Jesterisim]

i have a question. why is it suppose to be a+b=0 & a•b=0? is this a rule? does it work with every question?

[@asiasimpson70]

Xing AoShen He begins to explain at 4:39.

[@ytp1210]

yes its a rule

[@padraigbrady3521]

cleared everything up in less than 5 minutes for me. i would be lost without this man

[@rob494]

I love Khan Academy. I would be failing college algebra without them.

[@coolbro7695]

I like how your name is just Rob.

[@meooorw8801]

Rob this is for highschool though

[@Soren-i1m]

Rob this is grade 9 class algebra

[@LucasAlves-hi2kx]

@@meooorw8801 You still need to understand algebra concepts for calculus though

[@meooorw8801]

@@LucasAlves-hi2kx ye sorry

[@emimh6060]

He explains it wayy better than my teacher. He makes it easier but isnt quadractic formula the same? I know how to do that but this I still dont understand.

[@zzzz5929]

God bless you. Got an A on my test.

[@manasafromhogwarts6812]

THANK GOD FOR THIS VIDEO

[@BrainGainzOfficial]

Some topics in mathematics just make me so sad... Parallel lines, for example. They have so much in common, but they’ll never meet!

[@aiden5729]

you get me real good man reall funni man yes yes cool

[@bluqua]

Thank you so much, you saved me! This is the ONLY video that actually explains everything step-by-step without assuming that students know something when they actually don't. Very clear and easy to understand, thanks!

[@nickcolejackson6884]

I am n Calculus and I had to go back to these quadratics because once one gets into this higher level of math he/she still has to go back to these simple problem. I had forgot about these quadratics that continuously keeps coming back. Thank You for helping me, I understand the concept both ways completely.

[@MSFR-911_]

سبحان الله وبحمده سبحان الله العظيم استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ

[@Devaki888]

Tanks a lot It really helps though it is complicated at first

[@minthra870]

this didn't help me at all

[@hughmungus7690]

same

[@cesaramaya1234567]

Hugh Mungus same

[@arizonaprince6906]

rip

[@michaelmccorkle4062]

Im a math teacher. It's two numbers multiplied = -35 and added = -2

[@5000subsnovideo]

watch other vids. this guy overcomplicated it.

[@rajkecy2223]

How to solve this quadractic equation: (a-b)x^2-(a+b)x+2b=0. Anyone help please..

[@TotliTotli]

So you have to see what A and B must be? What if the problem is more complex and doesn't give such an easy answer.

[@conpa18dany]

Oh mathematics! I forgot how rewarding you are after the subject is mastered. I get a big smile on my face when I solve these problems.

[@karthikkumaravel4159]

How do I solve 4.9t squared + 14.7t - 137.2 = 0

[@adfxceedfgdfvvbasdfrtvcx]

This is probably too late to help you with your homework, but if you consider the question as 49t^2 + 147t-1372 you can simplify the problem to 49 (x^2 + 3 x - 28). Then solve from there the part within brackets which should get you on your way to the answer. Good luck.

[@david.ricardo]

Why we cant solve quadratic equations with traditional methods?

[@cefb8923]

This is what I really hate about learning math, there is never explanation of WHY were doing any of it. Why can't you solve it the traditional way?

[@zzurved]

@@cefb8923 same

[@-caesarian-6078]

@@cefb8923 / The point of these longer methods is to help with understanding why the method works. It is asking you to know the logic behind each step to make it easier to remember and apply to other problems. The old system showed the quickest way to do it, and wanted you to memorize each step of the process. I don’t yet know if the new way is better or worse.

[@nafishy]

it's very complicated😕

[@KidFoThaWin]

How the hell did he get from -7(s+5) to (s-7) by multiplying by s at around 2:40?????????????

[@fayehemanshi7177]

Rayshonda Hedgeh hey He took common or find similar numbers in the equation above. He took s common from s² + 5s which is s(s + 5). Then took 7 common from 7s-35 Here 35 is divisible by 7 by 5 times so 7(s + 5) And then here we need two values for s first we take s+5 and then s-7

[@leilocked]

I can't get though this without sleeping. I hate math T.T

[@emilyzhang4364]

I am a pre-middle schooler learning ahead of curriculum, this really helped

[@carteradams43]

How are you doing now?

[@emilyzhang4364]

@@carteradams43 i'm doing well! wow, it's been a few years, I forgot I even commented this :)

[@hergreeneyes]

That "s" and 5 made it hard to follow at times, for me.

[@saaniyahsajed1932]

Thanks so much, I have an Algebra final tomorrow and I needed to get a few things cleared up in my head! :)

[@SuperMegaLamp]

You're lucky to have remembered those things long ago

[@shlop1904]

gotta love it when your algebra 1 teacher was a terrible teacher so you barely know the basics so you gotta watch all these videos to have a clue of what to do :). Thanks khan academy

[@syamshorts8365]

Same

[@Stranger23397]

2:22 CAN SOMEONE EXPLAIN THIS TO ME!!! How do go from *s(s+5)-7(s+5)* to *(s+5)(s-7)* ??

[@nyleshamsi4465]

you combine the both the (s + 5) into one. you then just connect s and -7 to form (s - 7) put them together and it becomes (s + 5)(s - 7)

[@smileysmultimedia]

At that point in the problem where you've factored the equation and got a common factor from both groups, you need to further factor out the common factor. In this case the (s+5). As Rotten Potato said, the factors(numbers and/or variables) left outside the parenthesis put those together in their own parenthesis. You end up with a equation times and equation "(a + b)(x - z)". In this quadratic equation we're equaling to zero, so take both equations out of their parenthesis and put "= 0" on both. Solve the simple equations for your answer(s)

[@KidFoThaWin]

Rotten Potato what does that mean?????

[@theleakerbot]

Basically you can’t have two same values so convert the second value into the number being multiplied with the second value

[@PeterZ3000]

He lost me at "undistribute". :-( Otherwise, I love the videos.

[@cefb8923]

Same here.

[@PrincessOliverOfficial]

Isn't it easier to do the quadratic formula??

[@harryzhang1960]

Ya

[@oletra7695]

Nice video.

[@mattsmith6828]

these types of equations can be solved in theta log(n) time........ NO NEED FOR GUESS AND CHECK! sourceforge.net/projects/dougtrinom/files/FACTOR.8xp/download

[@teyzx123]

how would this even work for (5x^2 - 6x + 1). In this case. a + b = -6, while a.b is equal to 1. so it be (-5)+(-1)= -6 however, (-5).(-1) would not equal to 1.Even if i were to use other numbers it will not fulfill both requirements, so please correct me here what am i doing wrong using ur specific solution.

[@tamika1]

made this to complicated it is a easier way to explain this without doing all those extra steps

[@sureshaRekha]

Solve the following quadratic equation for x : x^2 + (a/a+b+a+b/a)x + 1

[@Xantexhunter]

I didn't understand any of this.

[@vicwang271]

Xantexhunter why

[@micheledempsey12]

man im sorry but your videos are WAY too complicated. you talk too fast and assume we know certain things and don't explain some steps.

[@BEEF-mr1eg]

I just got out of 7th grade and am studying this for next year. I don't like how difficult this is.

[@Jakewhat]

Are there any videos where he uses the actual quadratic equation because this is much harder than just using the actual quadratic equation.

[@carobear3537]

amazing how math never really changes

[@justinmaduako4315]

👍🏿✅ 💯💯. Sincerely, Justin Maduako

[@kelakotana]

If people don’t know what’s happening: s^2 - 2s - 35 = 0 Let’s say it like this. a + b = -2 and ab = -35 This means either a or b will be negative. But how do we find out. Simple, list out the factors of 35. The unique combo is 5 and -7. 5 + (-7) is -3and 5 x (-7) is 35. So we have this equation. s^2 +5s - 7s -35. Now what now. I like to put these into pairs and figure out what common factor they have, aka. factoring. So s^2 and 5s have a common factor of s so we get this. s(s+5) We can do the same thing to -7s - 35 using (-7) so we get -7(s+5) So we get this: s(s+5) - 7(s+5) Because we already have the factor of s + 5, we don’t need it, so we remove this, get the two numbers outside the parenthesis and make that a factor: (s + 5)(s - 7) Now let’s make it so these expressions equal zero. -5 and 7. These are our solutions for s. We can double check this as well. 49 (7 squared) - 14 (-2 x 7) - 35 = 0 25 (-5 squared) + 10 (-2 x -5) - 35 = 0

[@eminemworthy]

use this formula, it works for any quadratic, -b plus or minus root b^2-4ac/2a were a+b+c=0 i get 9+-root 81-144/4. which esentially simplifies to 9+-root-63/4 however you cant root a negative number unless you use the term j for all you electrical engineers which is equal to root -1.

[@onedgivesmelife5741]

Philippine educational system sucks we get college lessons as high school ones -_-

[@gabrielcodina5466]

Extremely helpful.

[@gabrielcodina5466]

Teacher had me confused all day.

[@cefb8923]

Everything kind of made sense until 2:24.. then suddenly it made no sense to me.

[@thewumpusswoo]

why was i told to watch this video for algebra when my teacher already taught us how to solve this

[@Lilmehh]

I don't even know what is he talking about sleepy teacher😂

[@kevinjohnson5430]

Yeah I agree I have been struggling on this math so badly that I didn't get what it meant?

[@SelfImprovement-o7o]

In India we say it as, The Splitting middle term method!!

[@kevinayala9393]

Honestly, didn't help at all, still super confused.

[@ming2k]

Back in 1980s when I was in junior high, one of my math teachers in China taught us below formula to solve any quadratic equations ax^2 + bx + c = 0, then we have (-b/(2a) - u)(-b/(2a) + u) = c/a, then we have (u + b/(2a))(u - b/(2a)) = -c/a. Solve the u we will get x = -b/(2a) - u or x = -b/(2a) + u.

[@reesriska]

@Everyone cant we just use asterisks method to do this?

[@siddanalokesh3972]

hey I you what is meaning of equation

[@melisaeren5809]

the given problem/question, for example: 5 + 5 = ? is an equation that you have to solve

[@Wentrashane]

So, if you didn't do the factoring by grouping, first, how do you get the numbers for the straight factoring method? It seems like that would have to be a -guess and check situation- which could take almost as long as the grouping method? Am I wrong? Please, correct if I am, because I want to better understand.

[@Berrypunch3]

It would be a lot simpler just to use the shortcut. :/ But maybe that complicated way will be of use in the future. Who knows?

[@johnnydinglenut]

why are all the comments about how people are dumb

[@MrLagvag]

yea im still a little confused, how did u get the 7 alone?. sorry math is very troubling for me, ever since i was a kid i had trouble comprehending math, and obviously it still carries on.

[@KP-rh5qz]

I learned this so differently in college. Probably because this was in 1993.

[@benr3799]

I’m 22 years old and still don’t know this by heart. And I consider myself math minded. I get tripped up trying to figure out how to factor when the leading coefficient of x^2 is not 1. The guessing game is the most difficult part for me at that point, I know there’s a shortcut but I don’t know it well enough to whip it out at anytime.

[@Blueian742]

So in this case the variable (s) equals the inverses of the two numbers you initially used in factoring out? Couldn’t you do this with other equations? Cause if so that’s a major short cut.

[@reesriska]

Cant we just use asterisks method on this????

[@Varun-hw2yr]

how to use factoring method for equations when coefficient of x^2 is not 1....e.g. 3x^2-10x+3=0

[@xMari95x]

FAVORITED! I have a stupid math teacher, who can't teach to save his LIFE.

[@social.b]

slow down and explain each step more please.

[@jokesthecat]

How did you get the S+5 and s-7 =0

[@Xasperato]

Quadratics is so counter-intuitive, it's a real pain-in-the-ass to learn. Despite that, I think I understand this part of it to a useful extent thanks to you. Your videos sure beat trying to read my illegible notes.

[@Thunder-wd6tm]

OMG this actually helps, I was so confused about this one, THANKS!

[@TheWiery322]

i understand that -35 is the same thing as 5*-7 but how in the hell does he just eliminate a giant factor of the problem. it just goes to dust

[@ProfBritz]

ax^2+bx+c=0. Find 2 numbers adding to b and multiplying to (a * c). Call those two numbers r & s. Then set up bx = rx + sx so that you have ax^2+rx+sx+c=0. Then you factor by grouping.

[@ErinStevens-o3g]

2:35 is where I have no clue why this is supposed to work

[@xaviert.123]

No clue either. I could be wrong but the way I see it, is like this: There are two terms that are the same in the formula s(s+5)-7(s+5) See how we have the s and the -7 outside of brackets? My theory is that for whatever reason, one of the (s+5) terms can be eliminated and replaced with the s and -7 combined, to make (s-7) So you have the s(s+5)-7(s+5), remove one of the s+5, replace it with the terms outside the brackets, and make that into a bracket. I could be entirely wrong so please take this with a pinch of salt, but this is how I interpret it

[@PeterZ3000]

@PeterZ3000 Now I get it. Had to watch "Factor by Grouping and Factoring Completely" to understand better.

[@Syntaxxed]

tastyyy and nutritious math thanks khan academy! I donated my past exams but will donate again soon. Your clear voice and explanation really makes me love math.

[@akhil___abi3349]

2:03 how does it become (s+5) instead of becoming (s-5)??

[@somerandomguy4436]

U can't get -35 if u use s-5 cuz the answer will be +35. In multiplication, same sign is + and diff sign is - ( no matter what sign they have)

[@sarahelizabeth8045]

What if it equals five and not 0?

[@kseniasmirnova4255]

не легче по формуле дискриминанта?

[@ShiftPC]

bro def not getting paif enough

[@korokojul]

still dont know whats going on..

[@carnat9565]

I was watching this while my tutorBeas watching me and didn't say anything u did a better job than them

[@vamrack8344]

This video helped make me understand a little

[@Tapeorchestraa]

still dont understand a thing

[@andredeleon1374]

People are doing this for college tests yet i am doing only for a year 8 test

[@jackwilson4324]

Did you really need to factor by grouping with a leading coefficient of 1?

[@SaleemCK]

Why not use X instead of S?

[@jazzhands6055]

made it way too complicated

[@sheilapaucar7067]

The thing is that a is 6, except that I'm good but I can't do this

[@SSR117]

def failing my exam tmr

[@Manperor]

Dang this was 10 years ago

[@iamcatrina]

how do you understand this i still don't get it 😭😭

[@omarhatem9575]

Did you watch the videos about factoring quadratics, if not, then you have like 15-20 videos you need to watch before this one.

[@eloi377]

This Video is way better than my teacher Thank you

[@angelesperancilla5010]

ac method is simpler

[@jacobkrakauer6954]

Im so lost in the sauce

[@chuayingkiat3586]

It took me 2min looking at an answer sheet to understand this