Question

Solve for all values of xx by factoring.
x, squared, plus, 6, x, minus, 12, equals, 4
x
2
+6x−12=
4

Answer 1

To solve the equation \( x^2 + 6x - 12 = 4 \) by factoring, we first need to set the equation equal to zero.

Subtract 4 from both sides:

\[
x^2 + 6x - 12 - 4 = 0
\]

This simplifies to:

\[
x^2 + 6x - 16 = 0
\]

Next, we factor the quadratic expression \( x^2 + 6x - 16 \). We need two numbers that multiply to \(-16\) (the constant term) and add to \(6\) (the coefficient of \(x\)).

The numbers \(8\) and \(-2\) meet these conditions because:

\[
8 \cdot (-2) = -16 \quad \text{and} \quad 8 + (-2) = 6
\]

Thus, we can factor the quadratic as follows:

\[
(x + 8)(x - 2) = 0
\]

Now, we set each factor equal to zero:

1. \( x + 8 = 0 \)
- This gives \( x = -8 \)

2. \( x - 2 = 0 \)
- This gives \( x = 2 \)

Therefore, the solutions to the equation \( x^2 + 6x - 12 = 4 \) are:

\[
\boxed{-8 \text{ and } 2}
\]