Solve Using the Square Root Property x^2=(-1)^2

$x^{2} = {(- 1)}^{2}$

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| x | = | - 1 |$

Solve for $x$ .

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x = \pm | - 1 |$

The absolute value is the distance between a number and zero. The distance between $- 1$ and $0$ is $1$ .

$x = \pm 1$

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.

$x = 1$

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

$x = - 1$

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

$x = 1, - 1$