Question

Solve x^2-7x=-12

a. x=2 and x=6
b. x=6 and x=-2
c. x=-4 and x=-3
d. x=4 and x=3

Answer 1

D. x = 4 and x = 3

Explanation:

The first step is to add 12 to both sides, like so:

`x^2 - 7x = -12\\`

+12 + 12

___________

`x^2` - 7x + 12 = 0

Split the middle term (7x) into two numbers that can be multiplied to get 12, and be added to get 7:

`x^2` - 4x - 3x + 12 = 0

Group:

(
`x^2` - 4x) (-3x + 12) = 0

Take out GCF (Greatest Common Factor):

x(x - 4) -3(x - 4) = 0

(x - 3) (x - 4) = 0

Set them both equal to 0:

x - 3 = 0 x - 4 = 0

+ 3 + 3 + 4 + 4

________ _______

x = 3 x = 4