Solve Using the Quadratic Formula -2x^2-16x-44=0

$- 2 x^{2} - 16 x - 44 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = - 2$ , $b = - 16$ , and $c = - 44$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (- 2 \cdot - 44)}}{2 \cdot - 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot - 2 \cdot - 44}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot - 44$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{16 \pm \sqrt{256 + 8 \cdot - 44}}{2 \cdot - 2}$

Multiply $8$ by $- 44$ .

$x = \frac{16 \pm \sqrt{256 - 352}}{2 \cdot - 2}$

Subtract $352$ from $256$ .

$x = \frac{16 \pm \sqrt{- 96}}{2 \cdot - 2}$

Rewrite $- 96$ as $- 1 (96)$ .

$x = \frac{16 \pm \sqrt{- 1 \cdot 96}}{2 \cdot - 2}$

Rewrite $\sqrt{- 1 (96)}$ as $\sqrt{- 1} \cdot \sqrt{96}$ .

$x = \frac{16 \pm \sqrt{- 1} \cdot \sqrt{96}}{2 \cdot - 2}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{16 \pm i \cdot \sqrt{96}}{2 \cdot - 2}$

Rewrite $96$ as $4^{2} \cdot 6$ .

Factor $16$ out of $96$ .

$x = \frac{16 \pm i \cdot \sqrt{16 (6)}}{2 \cdot - 2}$

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

$x = \frac{16 \pm i \cdot \sqrt{4^{2} \cdot 6}}{2 \cdot - 2}$

Pull terms out from under the radical.

$x = \frac{16 \pm i \cdot (4 \sqrt{6})}{2 \cdot - 2}$

Move $4$ to the left of $i$ .

$x = \frac{16 \pm 4 i \sqrt{6}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{16 \pm 4 i \sqrt{6}}{- 4}$

Simplify $\frac{16 \pm 4 i \sqrt{6}}{- 4}$ .

$x = \frac{4 \pm i \sqrt{6}}{- 1}$

Move the negative one from the denominator of $\frac{4 \pm i \sqrt{6}}{- 1}$ .

$x = - 1 \cdot (4 \pm i \sqrt{6})$

Rewrite $- 1 \cdot (4 \pm i \sqrt{6})$ as $- (4 \pm i \sqrt{6})$ .

$x = - (4 \pm i \sqrt{6})$