Solve Using the Square Root Property x^2=-20

$x^{2} = - 20$

Step 1

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

$x = \pm \sqrt{- 20}$

Step 2

Simplify $\pm \sqrt{- 20}$ .

Rewrite $- 20$ as $- 1 (20)$ .

$x = \pm \sqrt{- 1 (20)}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{20}$

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

$x = \pm i \cdot \sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$x = \pm i \cdot \sqrt{4 (5)}$

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

$x = \pm i \cdot \sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$x = \pm i \cdot (2 \sqrt{5})$

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

$x = \pm 2 i \sqrt{5}$

Step 3

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.

$x = 2 i \sqrt{5}$

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

$x = - 2 i \sqrt{5}$

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

$x = 2 i \sqrt{5}, - 2 i \sqrt{5}$