Solve Using the Quadratic Formula x^2+12x=-32

$x^{2} + 12 x = - 32$

Step 1

Add $32$ to both sides of the equation.

$x^{2} + 12 x + 32 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 12$ , and $c = 32$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (1 \cdot 32)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 1 \cdot 32}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 32$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 32}}{2 \cdot 1}$

Multiply $- 4$ by $32$ .

$x = \frac{- 12 \pm \sqrt{144 - 128}}{2 \cdot 1}$

Subtract $128$ from $144$ .

$x = \frac{- 12 \pm \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{- 12 \pm \sqrt{4^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 12 \pm 4}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 12 \pm 4}{2}$

Simplify $\frac{- 12 \pm 4}{2}$ .

$x = - 6 \pm 2$

Step 5

The final answer is the combination of both solutions.

$x = - 4, - 8$