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

Answer:

D. x = 4 and x = 3

Step-by-step 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