Precalculus Examples

$x^{4} - 4 = 0$

Step 1

Add $4$ to both sides of the equation.

$x^{4} = 4$

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

$x = \pm \sqrt{2}$

Step 4

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

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Step 4.1

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

$x = \sqrt{2}$

Step 4.2

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

$x = - \sqrt{2}$

Step 4.3

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.41421356 \dots, - 1.41421356 \dots$

Step 6