Solve Using the Square Root Property 2x^2-4=-12

$2 x^{2} - 4 = - 12$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$2 x^{2} = - 12 + 4$

Add $- 12$ and $4$ .

$2 x^{2} = - 8$

Step 2

Divide each term in $2 x^{2} = - 8$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 8$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 8}{2}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x^{2} = - 4$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{- 4}$

Step 4

Simplify $\pm \sqrt{- 4}$ .

Rewrite $- 4$ as $- 1 (4)$ .

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

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

$x = \pm \sqrt{- 1} \cdot \sqrt{4}$

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

$x = \pm i \cdot \sqrt{4}$

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

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

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

$x = \pm i \cdot 2$

Move $2$ to the left of $i$ .

$x = \pm 2 i$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 2 i$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 2 i$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 2 i, - 2 i$