Finite Math Examples

$f (x) = | x^{2} - 4 |$

Step 1

Set $| x^{2} - 4 |$ equal to $0$ .

$| x^{2} - 4 | = 0$

Step 2

Solve for $x$ .

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Step 2.1

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

$x^{2} - 4 = \pm 0$

Step 2.2

Plus or minus $0$ is $0$ .

$x^{2} - 4 = 0$

Step 2.3

Add $4$ to both sides of the equation.

$x^{2} = 4$

Step 2.4

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

$x = \pm \sqrt{4}$

Step 2.5

Simplify $\pm \sqrt{4}$ .

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Step 2.5.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.5.2

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

$x = \pm 2$

Step 2.6

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

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Step 2.6.1

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

$x = 2$

Step 2.6.2

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

$x = - 2$

Step 2.6.3

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

$x = 2, - 2$

Step 3