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# Solving quadratic equations by factoring (old)

An old video where Sal solves a bunch of quadratic equations by using factorization methods. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• why they call quadratic?.
• It's a bit strange to have such a geometric word in the middle of algebra, but quadratic means that it's about squares, here specifically that it involves expressions where you are squaring the independent variable.
• In the beginning of the video he mentions that in the previous video they show you something. My question is, is there a previous video? Isn't this the first one in "Multiplying and Factoring Expressions"?
• You will find the concept in Factoring Quadratic Expressions. Good luck.
• Why does Sal say( x-12)^2=0 then he says it like this: x-12=0 where is the ^2?
• Consider this: For (x-12)(x-12) to be equal to zero, one of those factors have to be zero.

Ie; one of them will have to be "X=1 2; X-12 = 12-12 = 0" for it to be Zero when solved.

We see that the factors that Sal arrives at are (X-12)(X-12): Both are the same, which means their product is equal to one of them being squared. Since both the factors are equal to Zero, even if one of them is removed, the resulting number on the RHS will be Zero.

This is why Sal states that they are both the same and that (x-12) = 0. Since one of them is 0, squaring still leaves us with the solution zero. It's like two people saying the same thing in a language, with different accents.

PS: Hope this makes sense. This is how I understand the concept. If I am wrong, correct me by all means! :)
(1 vote)
• what if you put 0/0=
• Why do you set quadratic equations equal to zero?
• Lots of things multiply to become a number:
21=3*7 and 21=(21/5)(1/5). This makes an infinite number of answers that equal 21.

However, only specific things multiply to equal 0. In fact, they are only things that involve a zero! (x+7)(x-3)=0 implies that one of those two factors is 0. So the next step is to solve the two factors for x:

(x+7)=0 and (x-3)=0

x+7=0 → x=-7
x-3=0 → x=3

Therefore, the final answer is you solve for x is:
x={-7,3} which is read as, ex is equal to the set that contains negative seven and three.

However, the question may not ask what x is. If it only asks what the fully factored form is, the answer is: (x+7)(x-3)=0
• find the value of unknown variable ,if
xy=2 and x+y=3
• The first thing to do when you face a problem like this is to test "easy solutions". I won't go in details of my thinking method, but the answer come right into my mind.

What two simple numbers multiplied give two? one and two. I then try them in the second equation, and it fills the solution.
x=1, y=2. There might be more solutions, but they were not asked.
• What if the coefficient of the first term is larger than 1?
• could someone please tell me about the rules. Ex: (a-b)(a+b)
• ``(a + b)(a + b) = a^2 + 2ab + b^2(a - b)(a - b) = a^2 - 2ab + b^2(a + b)(a - b) = a^2 - b^2``

If you don't remember the rules, figuring them out is not very difficult. The rules of multiplication are used. E.g.
(a + b)(a - b) =
a(a - b) + b(a - b) =
(a^2 - ab) + (ab - b^2) =
a^2 - ab + ab - b^2 =
a^2 - b^2