Solve for x 2x^4-32=0

$2 x^{4} - 32 = 0$

Step 1

Add $32$ to both sides of the equation.

$2 x^{4} = 32$

Step 2

Divide each term in $2 x^{4} = 32$ by $2$ and simplify.

Divide each term in $2 x^{4} = 32$ by $2$ .

$\frac{2 x^{4}}{2} = \frac{32}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x^{4}}{2} = \frac{32}{2}$

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

$x^{4} = \frac{32}{2}$

Simplify the right side.

Divide $32$ by $2$ .

$x^{4} = 16$

Step 3

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

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

Step 4

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

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

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

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$