Solving a quadratic equation by factoring | Algebra II

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

Рет қаралды 1,988,618

14 жыл бұрын

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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!
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Пікірлер: 281

@sevenisacannibal 6 жыл бұрын

guess i'll just die.

@shoaibkhan-qx3oq 2 жыл бұрын

its been 3 years are you dead

@omarkhattab5230 2 жыл бұрын

Yeah same

@sevenisacannibal 2 жыл бұрын

@@shoaibkhan-qx3oq only on the inside.

@youtubeenjoyer5083 Ай бұрын

@@sevenisacannibal still?

@shawtylikeamonke Ай бұрын

@@youtubeenjoyer5083i am

@face112 10 жыл бұрын

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

@russiangravy3870 3 жыл бұрын

Dork

@preparator9925 3 жыл бұрын

Its almost poetic

@sherrydiep839 3 жыл бұрын

@@preparator9925 facts

@laurenbethune2318 9 жыл бұрын

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

@ThePussukka 9 жыл бұрын

kzfaq.info/get/bejne/jp1yktd5mbWRj6c.html this helped me to understand this video

@vicwang271 7 жыл бұрын

Lauren Bethune are you dumb?

@laurenbethune2318 7 жыл бұрын

Vic Wang apparently

@vicwang271 7 жыл бұрын

Lauren Bethune what do you mean apparently

@laurenbethune2318 7 жыл бұрын

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?

@insaneshadow85 9 жыл бұрын

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 7 жыл бұрын

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

@davidk1308 7 жыл бұрын

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

@itsbk6192 5 жыл бұрын

So Did you?

@Goosiepoo 3 жыл бұрын

We need to know

@universalyoutuber195 3 жыл бұрын

Did you do it?

@onedgivesmelife5741 7 жыл бұрын

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

@vicwang271 7 жыл бұрын

yna how????

@david.ricardo 5 жыл бұрын

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

@evie5375 3 жыл бұрын

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

@enixepyx9001 3 жыл бұрын

@@david.ricardo chillllllllll mate

@omaralkindi1315 3 жыл бұрын

@@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.

@padraigbrady3521 6 жыл бұрын

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

@bluqua 13 жыл бұрын

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!

@izu1489 5 жыл бұрын

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

@universalyoutuber195 3 жыл бұрын

It’s been 2 years did they grow?

@hemavathi1028 3 жыл бұрын

@@universalyoutuber195 lmao

@izu1489 2 жыл бұрын

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

@TheWiery322 7 жыл бұрын

im completely lost i have no idea whats happening

@vardag3196 3 жыл бұрын

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 3 жыл бұрын

@@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 3 жыл бұрын

@@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 3 жыл бұрын

@@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

@rob494 8 жыл бұрын

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

@coolbro7695 6 жыл бұрын

I like how your name is just Rob.

@meooorw8801 6 жыл бұрын

Rob this is for highschool though

@user-re5ut3bg9u 6 жыл бұрын

Rob this is grade 9 class algebra

@LucasAlves-hi2kx 5 жыл бұрын

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

@meooorw8801 5 жыл бұрын

@@LucasAlves-hi2kx ye sorry

@zzzz5929 8 жыл бұрын

God bless you. Got an A on my test.

@GetUpAndWatchVideos 7 жыл бұрын

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

@Bee23447 3 жыл бұрын

My personal recommendation to fixing your problem, Slong = Toaster

@conpa18dany 8 жыл бұрын

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.

@ryanissa3353 4 жыл бұрын

Who else is here for an assignment?

@ricky_boi64 4 жыл бұрын

Yep

@abayerr279 4 жыл бұрын

Yessir

@kaihaughey4008 3 жыл бұрын

Mhm

@nickcolejackson6884 9 жыл бұрын

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.

@manasafromhogwarts6812 8 жыл бұрын

THANK GOD FOR THIS VIDEO

@nniiania 3 жыл бұрын

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

@Wentrashane 3 жыл бұрын

Exactly

@Goosiepoo 3 жыл бұрын

Yep

@emimh6060 7 жыл бұрын

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.

@Devaki888 4 жыл бұрын

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

@Thunder-wd6tm 3 жыл бұрын

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

@mickey040404 11 жыл бұрын

i totally understand my whole factoring projet for Algebra II now. thank you soooo much.

@saaniyahsajed1932 8 жыл бұрын

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

@SuperMegaLamp 3 жыл бұрын

You're lucky to have remembered those things long ago

@hmbasharat 6 жыл бұрын

Thank you, great resource, just solved my problem

@shlop1904 3 жыл бұрын

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 Жыл бұрын

Same

@Herpderpface13 12 жыл бұрын

Your really good at teaching this!!

@Syntaxxed 2 жыл бұрын

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.

@sanskar49 7 жыл бұрын

Thanks for this tutorial!!!!!!!!!!

@carobear3537 5 жыл бұрын

amazing how math never really changes

@vamrack8344 6 жыл бұрын

This video helped make me understand a little

@XingAoShen 9 жыл бұрын

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 9 жыл бұрын

Xing AoShen He begins to explain at 4:39.

@ytp1210 8 жыл бұрын

yes its a rule

@katsphws 12 жыл бұрын

Thank you VERY VERY much for your videos.

@PC_Principal 13 жыл бұрын

Thanks man ur a big help.

@taters1123 12 жыл бұрын

When factored, 2x^2- 9x- 18 ends up being (2x + 3)(x - 6) using Khan's factoring method. From there, you can deduce that X=6 and X= -1.5

@Xasperato 9 жыл бұрын

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.

@ming2k 2 жыл бұрын

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.

@kitanomarumilitoni9293 7 жыл бұрын

Thank you so much, i understand it a little better now lol

@halehagdassi4682 6 жыл бұрын

Great Video! Makes Sense!

@gabrielcodina5466 6 жыл бұрын

Extremely helpful.

@gabrielcodina5466 6 жыл бұрын

Teacher had me confused all day.

@eloi377 2 жыл бұрын

This Video is way better than my teacher Thank you

@MSFR-911_ 2 жыл бұрын

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

@oletra7695 8 жыл бұрын

Nice video.

@benr3799 2 жыл бұрын

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.

@TotliTotli 14 жыл бұрын

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.

@carnat9565 7 жыл бұрын

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

@razer4174 7 жыл бұрын

helps so much

@eminemworthy 12 жыл бұрын

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.

@LinvestigatesMC 10 жыл бұрын

do you use a slate when you write?

@ProfBritz 11 жыл бұрын

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.

@yoichiteamZ 11 ай бұрын

As a grade 4 student, thanks for finally clarifying everything to me !

@DazombieAlien 9 ай бұрын

YOU’RE LEARNING THIS IN THE FOURTH GRADE??

@Blueian742 Жыл бұрын

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.

@FugieGamers 8 жыл бұрын

Very helpful thanks!

@PeterZ3000 12 жыл бұрын

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

@rajkecy2223 5 жыл бұрын

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

@Wentrashane 3 жыл бұрын

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.

@andrewmadrigal2592 5 жыл бұрын

Thank you soooooo muuuuch

@kelakotana 4 жыл бұрын

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

@somelameartist7725 6 жыл бұрын

Bless you for this, I was stuck on a really easy part and now I understand! Thank you, thank you!!

@emilyzhang4364 4 жыл бұрын

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

@carteradams43 2 жыл бұрын

How are you doing now?

@emilyzhang4364 2 жыл бұрын

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

@noraizhossain5143 Жыл бұрын

i love your stuff g

@teyzx123 20 күн бұрын

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.

@Jakewhat 11 жыл бұрын

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

@Varun-hw2yr 8 жыл бұрын

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

@karthikkumaravel4159 4 жыл бұрын

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

@adfxceedfgdfvvbasdfrtvcx 4 жыл бұрын

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.

@BrainGainzOfficial 5 жыл бұрын

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 4 жыл бұрын

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

@bl9ze Жыл бұрын

Thanks

@user-he7ve4pg7x 4 ай бұрын

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

@m3rl1n97 6 жыл бұрын

Thanks pal :)

@paulceltics 13 жыл бұрын

thanks

@sarahgolts6911 8 жыл бұрын

Thank you for the helpful video. This really helped me get a grasp on the concept! :)

@BEEF-mr1eg Ай бұрын

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

@david.ricardo 5 жыл бұрын

Why we cant solve quadratic equations with traditional methods?

@cefb8923 3 жыл бұрын

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 3 жыл бұрын

@@cefb8923 same

@-caesarian-6078 3 жыл бұрын

@@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.

@MrLagvag 11 жыл бұрын

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.

@michaelmccorkle4062 5 жыл бұрын

Easy fun stuff

@tamika1 7 жыл бұрын

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

@Someone-dg7om 3 жыл бұрын

i have a test tmrw u saved my life

@Someone-dg7om 3 жыл бұрын

tytyty

@notmarcus17 3 жыл бұрын

How did you do? I have a final in a few days I am studying for

@Berrypunch3 7 жыл бұрын

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?

@justinmaduako4315 10 ай бұрын

👍🏿✅ 💯💯. Sincerely, Justin Maduako

@kevinjohnson5430 2 жыл бұрын

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

@leilocked 11 жыл бұрын

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

@mayahamandi4754 5 жыл бұрын

Thank you so much, this really helped me with my math test, this and other videos have been helping me through school

@social.b 3 жыл бұрын

slow down and explain each step more please.

@kseniasmirnova4255 3 жыл бұрын

не легче по формуле дискриминанта?

@MathanVasu 11 жыл бұрын

Can someone help me? How do you solve 2x^2 -11x + 15 = 0

@jackwilson4324 5 жыл бұрын

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

@happybro2802 3 жыл бұрын

Set❤️

@Stranger23397 7 жыл бұрын

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

@nyleshamsi4465 7 жыл бұрын

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 7 жыл бұрын

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 7 жыл бұрын

Rotten Potato what does that mean?????

@theleakerbot 5 жыл бұрын

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

@nafishy 5 жыл бұрын

it's very complicated😕

@jokesthecat Жыл бұрын

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

@reesriska 3 жыл бұрын

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

@PrincessOliverOfficial 7 жыл бұрын

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

@harryzhang1960 Жыл бұрын

@hergreeneyes 2 жыл бұрын

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

@KidFoThaWin 7 жыл бұрын

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

@fayehemanshi7177 5 жыл бұрын

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