Solve Using the Square Root Property x^2=-400

$x^{2} = - 400$

Step 1

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

$x = \pm \sqrt{- 400}$

Step 2

Simplify $\pm \sqrt{- 400}$ .

Rewrite $- 400$ as $- 1 (400)$ .

$x = \pm \sqrt{- 1 (400)}$

Rewrite $\sqrt{- 1 (400)}$ as $\sqrt{- 1} \cdot \sqrt{400}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{400}$

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

$x = \pm i \cdot \sqrt{400}$

Rewrite $400$ as $20^{2}$ .

$x = \pm i \cdot \sqrt{20^{2}}$

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

$x = \pm i \cdot 20$

Move $20$ to the left of $i$ .

$x = \pm 20 i$

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.

$x = 20 i$

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

$x = - 20 i$

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

$x = 20 i, - 20 i$