Solve Using the Square Root Property x^2+7=-300

$x^{2} + 7 = - 300$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$x^{2} = - 300 - 7$

Subtract $7$ from $- 300$ .

$x^{2} = - 307$

Step 2

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

$x = \pm \sqrt{- 307}$

Step 3

Simplify $\pm \sqrt{- 307}$ .

Rewrite $- 307$ as $- 1 (307)$ .

$x = \pm \sqrt{- 1 (307)}$

Rewrite $\sqrt{- 1 (307)}$ as $\sqrt{- 1} \cdot \sqrt{307}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{307}$

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

$x = \pm i \sqrt{307}$

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.

$x = i \sqrt{307}$

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

$x = - i \sqrt{307}$

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

$x = i \sqrt{307}, - i \sqrt{307}$