Solve the equation by factoring. Show all of your work to receive full credit. %0D%0A%0D%0Ax2+4x − 12=0%0D%0A%0D%0A2%0D%0A+%0D%0A4%0D%0A%0D%0A %0D%0A−%0D%0A %0D%0A12%0D%0A=%0D%0A0%0D%0A(2 points

Answer 1

To solve the equation x^2 + 4x - 12 = 0 by factoring, we need to find two numbers whose sum is 4 and whose product is -12.

Let's list all possible pairs of factors of -12:
1, -12
-1, 12
2, -6
-2, 6
3, -4
-3, 4

From these pairs, we can see that the pair 6 and -2 satisfies the sum condition. Therefore, we can rewrite the equation as:

(x + 6)(x - 2) = 0

Now, we set each factor equal to zero and solve for x:

x + 6 = 0
x = -6

x - 2 = 0
x = 2

Therefore, the solutions to the equation x^2 + 4x - 12 = 0 are x = -6 and x = 2.