Calculus Examples

$| x^{2} - 1 | = 0$

Step 1

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

$x^{2} - 1 = \pm 0$

Step 2

Plus or minus $0$ is $0$ .

$x^{2} - 1 = 0$

Step 3

Add $1$ to both sides of the equation.

$x^{2} = 1$

Step 4

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

$x = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x = \pm 1$

Step 6

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

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Step 6.2

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

$x = - 1$

Step 6.3

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

$x = 1, - 1$