Question

3x ^2-4x=4
Hi ( : can anyone walk me through how to solve for x?

Answer 1

The first thing you'll want to do is get the right side to equal 0. How can we do that?

Answer 2

subtract 4 from both sides?

Answer 3

Yes. Therefore, on the left side, we have:
3x^2 - 4x - 4 = 0
Because are relatively easy numbers, we can factor this.
So, what does it mean to factor? The zero product property comes in. When we have two things that are multiplied together and they equal 0, that means at least one has to be equal to 0.
Therefore, our equation can be written as:
(x + a)(x + b)
Or,
(x + some number)(x + some number)

Answer 4

But, since the leading coefficient of x is non-1, that means it has to be written as:
(ax+ somenumber)(x+ somenumber)

Answer 5

We can take a guess as to what this can be factored into. I'll "estimate":
(3x + 2)(x + 2)
If we expand this, we get:
3x^2 + 6x + 2x + 4 = 2x^2 + 8x + 4
This is kinda close, but not right. What do you think we can do to change it?

Answer 6

hm, should I find a number that adds to negative one and multiplies to 4?

Answer 7

Well, we're trying to make the "+4" into "-4", and "8x" to "6x". I'll give you the hint that the actual numbers are correct, but one sign needs to change for it to work out.

Answer 8

why 8x to 6x?

Answer 9

*facepalm* I meant -4x. I apologize.

Answer 10

no worries ( : haha so you would just change the sign after 2 on the left and after the 8x on the right? and add one in front of 2xx^2?

Answer 11

Yup. So your factorization is:
(3x - 2)(x + 2)
Now all you have to do is solve the equations:
3x - 2 = 0
x + 2 = 0
To obtain your possible answers for x.

Answer 12

2/3 for the first and 2 for the second

Answer 13

-2

Answer 14

Congladurations.

Answer 15

thanks bloopman c: