Solve for x x^2=-27

$x^{2} = - 27$

Step 1

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

$x = \pm \sqrt{- 27}$

Step 2

Simplify $\pm \sqrt{- 27}$ .

Rewrite $- 27$ as $- 1 (27)$ .

$x = \pm \sqrt{- 1 (27)}$

Rewrite $\sqrt{- 1 (27)}$ as $\sqrt{- 1} \cdot \sqrt{27}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{27}$

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

$x = \pm i \cdot \sqrt{27}$

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$x = \pm i \cdot \sqrt{9 (3)}$

Rewrite $9$ as $3^{2}$ .

$x = \pm i \cdot \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$x = \pm i \cdot (3 \sqrt{3})$

Move $3$ to the left of $i$ .

$x = \pm 3 i \sqrt{3}$

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.

$x = 3 i \sqrt{3}$

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

$x = - 3 i \sqrt{3}$

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

$x = 3 i \sqrt{3}, - 3 i \sqrt{3}$