Solve Using the Square Root Property 2x^2-7=-79

$2 x^{2} - 7 = - 79$

Step 1

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

Add $7$ to both sides of the equation.

$2 x^{2} = - 79 + 7$

Add $- 79$ and $7$ .

$2 x^{2} = - 72$

Step 2

Divide each term in $2 x^{2} = - 72$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 72$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 72}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 72}{2}$

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

$x^{2} = \frac{- 72}{2}$

Simplify the right side.

Divide $- 72$ by $2$ .

$x^{2} = - 36$

Step 3

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

$x = \pm \sqrt{- 36}$

Step 4

Simplify $\pm \sqrt{- 36}$ .

Rewrite $- 36$ as $- 1 (36)$ .

$x = \pm \sqrt{- 1 (36)}$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{36}$

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

$x = \pm i \cdot \sqrt{36}$

Rewrite $36$ as $6^{2}$ .

$x = \pm i \cdot \sqrt{6^{2}}$

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

$x = \pm i \cdot 6$

Move $6$ to the left of $i$ .

$x = \pm 6 i$

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.

$x = 6 i$

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

$x = - 6 i$

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

$x = 6 i, - 6 i$