Solve Using the Square Root Property 3x^2-5=-113

$3 x^{2} - 5 = - 113$

Step 1

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

Add $5$ to both sides of the equation.

$3 x^{2} = - 113 + 5$

Add $- 113$ and $5$ .

$3 x^{2} = - 108$

Step 2

Divide each term in $3 x^{2} = - 108$ by $3$ and simplify.

Divide each term in $3 x^{2} = - 108$ by $3$ .

$\frac{3 x^{2}}{3} = \frac{- 108}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} = \frac{- 108}{3}$

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

$x^{2} = \frac{- 108}{3}$

Simplify the right side.

Divide $- 108$ by $3$ .

$x^{2} = - 36$

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.

$x = 6 i, - 6 i$