Solve for x x^2=-96

$x^{2} = - 96$

Step 1

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

$x = \pm \sqrt{- 96}$

Step 2

Simplify $\pm \sqrt{- 96}$ .

Rewrite $- 96$ as $- 1 (96)$ .

$x = \pm \sqrt{- 1 (96)}$

Rewrite $\sqrt{- 1 (96)}$ as $\sqrt{- 1} \cdot \sqrt{96}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{96}$

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

$x = \pm i \cdot \sqrt{96}$

Rewrite $96$ as $4^{2} \cdot 6$ .

Factor $16$ out of $96$ .

$x = \pm i \cdot \sqrt{16 (6)}$

Rewrite $16$ as $4^{2}$ .

$x = \pm i \cdot \sqrt{4^{2} \cdot 6}$

Pull terms out from under the radical.

$x = \pm i \cdot (4 \sqrt{6})$

Move $4$ to the left of $i$ .

$x = \pm 4 i \sqrt{6}$

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.

$x = 4 i \sqrt{6}$

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

$x = - 4 i \sqrt{6}$

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

$x = 4 i \sqrt{6}, - 4 i \sqrt{6}$