Solve Using the Square Root Property 2x^2-3=-21

$2 x^{2} - 3 = - 21$

Step 1

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

Add $3$ to both sides of the equation.

$2 x^{2} = - 21 + 3$

Add $- 21$ and $3$ .

$2 x^{2} = - 18$

Step 2

Divide each term in $2 x^{2} = - 18$ by $2$ and simplify.

Divide each term in $2 x^{2} = - 18$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{- 18}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{- 18}{2}$

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

$x^{2} = \frac{- 18}{2}$

Simplify the right side.

Divide $- 18$ by $2$ .

$x^{2} = - 9$

Step 3

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

$x = \pm \sqrt{- 9}$

Step 4

Simplify $\pm \sqrt{- 9}$ .

Rewrite $- 9$ as $- 1 (9)$ .

$x = \pm \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{9}$

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

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

Rewrite $9$ as $3^{2}$ .

$x = \pm i \cdot \sqrt{3^{2}}$

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

$x = \pm i \cdot 3$

Move $3$ to the left of $i$ .

$x = \pm 3 i$

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.

$x = 3 i$

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

$x = - 3 i$

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

$x = 3 i, - 3 i$