Solve Using the Square Root Property x^2+121=0

$x^{2} + 121 = 0$

Step 1

Subtract $121$ from both sides of the equation.

$x^{2} = - 121$

Step 2

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

$x = \pm \sqrt{- 121}$

Step 3

Simplify $\pm \sqrt{- 121}$ .

Rewrite $- 121$ as $- 1 (121)$ .

$x = \pm \sqrt{- 1 (121)}$

Rewrite $\sqrt{- 1 (121)}$ as $\sqrt{- 1} \cdot \sqrt{121}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{121}$

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

$x = \pm i \cdot \sqrt{121}$

Rewrite $121$ as $11^{2}$ .

$x = \pm i \cdot \sqrt{11^{2}}$

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

$x = \pm i \cdot 11$

Move $11$ to the left of $i$ .

$x = \pm 11 i$

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.

$x = 11 i$

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

$x = - 11 i$

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

$x = 11 i, - 11 i$