Solve Using the Square Root Property 2x^2-9=-171

$2 x^{2} - 9 = - 171$

Step 1

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

Add $9$ to both sides of the equation.

$2 x^{2} = - 171 + 9$

Add $- 171$ and $9$ .

$2 x^{2} = - 162$

Step 2

Divide each term in $2 x^{2} = - 162$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 162$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 162}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 162}{2}$

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

$x^{2} = \frac{- 162}{2}$

Simplify the right side.

Divide $- 162$ by $2$ .

$x^{2} = - 81$

Step 3

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

$x = \pm \sqrt{- 81}$

Step 4

Simplify $\pm \sqrt{- 81}$ .

Rewrite $- 81$ as $- 1 (81)$ .

$x = \pm \sqrt{- 1 (81)}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{81}$

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

$x = \pm i \cdot \sqrt{81}$

Rewrite $81$ as $9^{2}$ .

$x = \pm i \cdot \sqrt{9^{2}}$

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

$x = \pm i \cdot 9$

Move $9$ to the left of $i$ .

$x = \pm 9 i$

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.

$x = 9 i$

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

$x = - 9 i$

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

$x = 9 i, - 9 i$