Solve Using the Quadratic Formula 2x^2+12x=-18

$2 x^{2} + 12 x = - 18$

Step 1

Add $18$ to both sides of the equation.

$2 x^{2} + 12 x + 18 = 0$

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 $a = 2$ , $b = 12$ , and $c = 18$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (2 \cdot 18)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 2 \cdot 18}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 18$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 8 \cdot 18}}{2 \cdot 2}$

Multiply $- 8$ by $18$ .

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

Subtract $144$ from $144$ .

$x = \frac{- 12 \pm \sqrt{0}}{2 \cdot 2}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{- 12 \pm \sqrt{0^{2}}}{2 \cdot 2}$

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

$x = \frac{- 12 \pm 0}{2 \cdot 2}$

$- 12$ plus or minus $0$ is $- 12$ .

$x = \frac{- 12}{2 \cdot 2}$

Multiply $2$ by $2$ .

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

Divide $- 12$ by $4$ .

$x = - 3$

Step 5

The final answer is the combination of both solutions.

$x = - 3$ Double roots