Solve Using the Square Root Property x^2=-100

$x^{2} = - 100$

Step 1

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

$x = \pm \sqrt{- 100}$

Step 2

Simplify $\pm \sqrt{- 100}$ .

Rewrite $- 100$ as $- 1 (100)$ .

$x = \pm \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{100}$

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

$x = \pm i \cdot \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$x = \pm i \cdot \sqrt{10^{2}}$

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

$x = \pm i \cdot 10$

Move $10$ to the left of $i$ .

$x = \pm 10 i$

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.

$x = 10 i$

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

$x = - 10 i$

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

$x = 10 i, - 10 i$