Solve for x 16x^4-1=0

$16 x^{4} - 1 = 0$

Step 1

Add $1$ to both sides of the equation.

$16 x^{4} = 1$

Step 2

Divide each term in $16 x^{4} = 1$ by $16$ and simplify.

Divide each term in $16 x^{4} = 1$ by $16$ .

$\frac{16 x^{4}}{16} = \frac{1}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x^{4}}{16} = \frac{1}{16}$

Divide $x^{4}$ by $1$ .

$x^{4} = \frac{1}{16}$

Step 3

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{\frac{1}{16}}$

Step 4

Simplify $\pm \sqrt[4]{\frac{1}{16}}$ .

Rewrite $\sqrt[4]{\frac{1}{16}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{16}}$ .

$x = \pm \frac{\sqrt[4]{1}}{\sqrt[4]{16}}$

Any root of $1$ is $1$ .

$x = \pm \frac{1}{\sqrt[4]{16}}$

Simplify the denominator.

Rewrite $16$ as $2^{4}$ .

$x = \pm \frac{1}{\sqrt[4]{2^{4}}}$

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

$x = \pm \frac{1}{2}$

Step 5

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.

$x = \frac{1}{2}$

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

$x = - \frac{1}{2}$

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

$x = \frac{1}{2}, - \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, - \frac{1}{2}$

Decimal Form:

$x = 0.5, - 0.5$