Solve Using the Square Root Property x^2+196=0

$x^{2} + 196 = 0$

Step 1

Subtract $196$ from both sides of the equation.

$x^{2} = - 196$

Step 2

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

$x = \pm \sqrt{- 196}$

Step 3

Simplify $\pm \sqrt{- 196}$ .

Rewrite $- 196$ as $- 1 (196)$ .

$x = \pm \sqrt{- 1 (196)}$

Rewrite $\sqrt{- 1 (196)}$ as $\sqrt{- 1} \cdot \sqrt{196}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{196}$

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

$x = \pm i \cdot \sqrt{196}$

Rewrite $196$ as $14^{2}$ .

$x = \pm i \cdot \sqrt{14^{2}}$

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

$x = \pm i \cdot 14$

Move $14$ to the left of $i$ .

$x = \pm 14 i$

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.

$x = 14 i$

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

$x = - 14 i$

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

$x = 14 i, - 14 i$