Solve Using the Square Root Property x^2+150=0

$x^{2} + 150 = 0$

Step 1

Subtract $150$ from both sides of the equation.

$x^{2} = - 150$

Step 2

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

$x = \pm \sqrt{- 150}$

Step 3

Simplify $\pm \sqrt{- 150}$ .

Rewrite $- 150$ as $- 1 (150)$ .

$x = \pm \sqrt{- 1 (150)}$

Rewrite $\sqrt{- 1 (150)}$ as $\sqrt{- 1} \cdot \sqrt{150}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{150}$

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

$x = \pm i \cdot \sqrt{150}$

Rewrite $150$ as $5^{2} \cdot 6$ .

Factor $25$ out of $150$ .

$x = \pm i \cdot \sqrt{25 (6)}$

Rewrite $25$ as $5^{2}$ .

$x = \pm i \cdot \sqrt{5^{2} \cdot 6}$

Pull terms out from under the radical.

$x = \pm i \cdot (5 \sqrt{6})$

Move $5$ to the left of $i$ .

$x = \pm 5 i \sqrt{6}$

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.

$x = 5 i \sqrt{6}$

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

$x = - 5 i \sqrt{6}$

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

$x = 5 i \sqrt{6}, - 5 i \sqrt{6}$