Solve Using the Quadratic Formula -2x^2-6=0

$- 2 x^{2} - 6 = 0$

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 $a = - 2$ , $b = 0$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 2 \cdot - 6)}}{2 \cdot - 2}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 2 \cdot - 6}}{2 \cdot - 2}$

Multiply $- 4 \cdot - 2 \cdot - 6$ .

Multiply $- 4$ by $- 2$ .

$x = \frac{0 \pm \sqrt{0 + 8 \cdot - 6}}{2 \cdot - 2}$

Multiply $8$ by $- 6$ .

$x = \frac{0 \pm \sqrt{0 - 48}}{2 \cdot - 2}$

Subtract $48$ from $0$ .

$x = \frac{0 \pm \sqrt{- 48}}{2 \cdot - 2}$

Rewrite $- 48$ as $- 1 (48)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 48}}{2 \cdot - 2}$

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{48}}{2 \cdot - 2}$

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

$x = \frac{0 \pm i \cdot \sqrt{48}}{2 \cdot - 2}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x = \frac{0 \pm i \cdot \sqrt{16 (3)}}{2 \cdot - 2}$

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

$x = \frac{0 \pm i \cdot \sqrt{4^{2} \cdot 3}}{2 \cdot - 2}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (4 \sqrt{3})}{2 \cdot - 2}$

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

$x = \frac{0 \pm 4 i \sqrt{3}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{0 \pm 4 i \sqrt{3}}{- 4}$

Simplify $\frac{0 \pm 4 i \sqrt{3}}{- 4}$ .

$x = \pm i \sqrt{3}$