Precalculus Examples

$f (x) = x^{4} - 25$

Step 1

Set $x^{4} - 25$ equal to $0$ .

$x^{4} - 25 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $25$ to both sides of the equation.

$x^{4} = 25$

Step 2.2

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

$x = \pm \sqrt[4]{25}$

Step 2.3

Simplify $\pm \sqrt[4]{25}$ .

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Step 2.3.1

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt[4]{5^{2}}$

Step 2.3.2

Rewrite $\sqrt[4]{5^{2}}$ as $\sqrt{\sqrt{5^{2}}}$ .

$x = \pm \sqrt{\sqrt{5^{2}}}$

Step 2.3.3

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

$x = \pm \sqrt{5}$

Step 2.4

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

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Step 2.4.1

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

$x = \sqrt{5}$

Step 2.4.2

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

$x = - \sqrt{5}$

Step 2.4.3

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

$x = \sqrt{5}, - \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{5}, - \sqrt{5}$

Decimal Form:

$x = 2.23606797 \dots, - 2.23606797 \dots$

Step 4