Solve Using the Square Root Property x^2=-169

$x^{2} = - 169$

Step 1

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

$x = \pm \sqrt{- 169}$

Step 2

Simplify $\pm \sqrt{- 169}$ .

Rewrite $- 169$ as $- 1 (169)$ .

$x = \pm \sqrt{- 1 (169)}$

Rewrite $\sqrt{- 1 (169)}$ as $\sqrt{- 1} \cdot \sqrt{169}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{169}$

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

$x = \pm i \cdot \sqrt{169}$

Rewrite $169$ as $13^{2}$ .

$x = \pm i \cdot \sqrt{13^{2}}$

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

$x = \pm i \cdot 13$

Move $13$ to the left of $i$ .

$x = \pm 13 i$

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.

$x = 13 i$

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

$x = - 13 i$

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

$x = 13 i, - 13 i$