Solve Using the Quadratic Formula 2x^2-7=-15

$2 x^{2} - 7 = - 15$

Step 1

Move all terms to the left side of the equation and simplify.

Add $15$ to both sides of the equation.

$2 x^{2} - 7 + 15 = 0$

Add $- 7$ and $15$ .

$2 x^{2} + 8 = 0$

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 $a = 2$ , $b = 0$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot 8)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot 8}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot 8$ .

Multiply $- 4$ by $2$ .

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

Multiply $- 8$ by $8$ .

$x = \frac{0 \pm \sqrt{0 - 64}}{2 \cdot 2}$

Subtract $64$ from $0$ .

$x = \frac{0 \pm \sqrt{- 64}}{2 \cdot 2}$

Rewrite $- 64$ as $- 1 (64)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 64}}{2 \cdot 2}$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{64}}{2 \cdot 2}$

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

$x = \frac{0 \pm i \cdot \sqrt{64}}{2 \cdot 2}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{8^{2}}}{2 \cdot 2}$

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

$x = \frac{0 \pm i \cdot 8}{2 \cdot 2}$

Move $8$ to the left of $i$ .

$x = \frac{0 \pm 8 i}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{0 \pm 8 i}{4}$

Simplify $\frac{0 \pm 8 i}{4}$ .

$x = \pm 2 i$