Solve Using the Square Root Property x^2=128

$x^{2} = 128$

Step 1

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

$x = \pm \sqrt{128}$

Step 2

Simplify $\pm \sqrt{128}$ .

Rewrite $128$ as $8^{2} \cdot 2$ .

Factor $64$ out of $128$ .

$x = \pm \sqrt{64 (2)}$

Rewrite $64$ as $8^{2}$ .

$x = \pm \sqrt{8^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm 8 \sqrt{2}$

Step 3

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.

$x = 8 \sqrt{2}$

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

$x = - 8 \sqrt{2}$

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

$x = 8 \sqrt{2}, - 8 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 8 \sqrt{2}, - 8 \sqrt{2}$

Decimal Form:

$x = 11.31370849 \dots, - 11.31370849 \dots$