Solve Using the Quadratic Formula 2(x^2-7)-2=2

$2 (x^{2} - 7) - 2 = 2$

Step 1

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

Simplify the left side.

Simplify $2 (x^{2} - 7) - 2$ .

Simplify each term.

Apply the distributive property.

$2 x^{2} + 2 \cdot - 7 - 2 = 2$

Multiply $2$ by $- 7$ .

$2 x^{2} - 14 - 2 = 2$

Subtract $2$ from $- 14$ .

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

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $- 16$ .

$2 x^{2} - 18 = 0$

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 $a = 2$ , $b = 0$ , and $c = - 18$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot - 18)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot - 18}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot - 18}}{2 \cdot 2}$

Multiply $- 8$ by $- 18$ .

$x = \frac{0 \pm \sqrt{0 + 144}}{2 \cdot 2}$

Add $0$ and $144$ .

$x = \frac{0 \pm \sqrt{144}}{2 \cdot 2}$

Rewrite $144$ as $12^{2}$ .

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

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

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

Multiply $2$ by $2$ .

$x = \frac{0 \pm 12}{4}$

Simplify $\frac{0 \pm 12}{4}$ .

$x = \pm 3$

Step 5

The final answer is the combination of both solutions.

$x = 3, - 3$