Solve Using the Square Root Property x^2+28=0

$x^{2} + 28 = 0$

Step 1

Subtract $28$ from both sides of the equation.

$x^{2} = - 28$

Step 2

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

$x = \pm \sqrt{- 28}$

Step 3

Simplify $\pm \sqrt{- 28}$ .

Rewrite $- 28$ as $- 1 (28)$ .

$x = \pm \sqrt{- 1 (28)}$

Rewrite $\sqrt{- 1 (28)}$ as $\sqrt{- 1} \cdot \sqrt{28}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{28}$

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

$x = \pm i \cdot \sqrt{28}$

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$x = \pm i \cdot \sqrt{4 (7)}$

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

$x = \pm i \cdot \sqrt{2^{2} \cdot 7}$

Pull terms out from under the radical.

$x = \pm i \cdot (2 \sqrt{7})$

Move $2$ to the left of $i$ .

$x = \pm 2 i \sqrt{7}$

Step 4

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.

$x = 2 i \sqrt{7}$

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

$x = - 2 i \sqrt{7}$

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

$x = 2 i \sqrt{7}, - 2 i \sqrt{7}$