Solve Using the Square Root Property x^2+225=0

$x^{2} + 225 = 0$

Step 1

Subtract $225$ from both sides of the equation.

$x^{2} = - 225$

Step 2

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

$x = \pm \sqrt{- 225}$

Step 3

Simplify $\pm \sqrt{- 225}$ .

Rewrite $- 225$ as $- 1 (225)$ .

$x = \pm \sqrt{- 1 (225)}$

Rewrite $\sqrt{- 1 (225)}$ as $\sqrt{- 1} \cdot \sqrt{225}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{225}$

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

$x = \pm i \cdot \sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$x = \pm i \cdot \sqrt{15^{2}}$

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

$x = \pm i \cdot 15$

Move $15$ to the left of $i$ .

$x = \pm 15 i$

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.

$x = 15 i$

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

$x = - 15 i$

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

$x = 15 i, - 15 i$