Solve Using the Quadratic Formula x^4-81

$x^{4} - 81$

Step 1

Set $x^{4} - 81$ equal to $0$ .

$x^{4} - 81 = 0$

Step 2

Add $81$ to both sides of the equation.

$x^{4} = 81$

Step 3

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

$x = \pm \sqrt[4]{81}$

Step 4

Simplify $\pm \sqrt[4]{81}$ .

Rewrite $81$ as $3^{4}$ .

$x = \pm \sqrt[4]{3^{4}}$

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

$x = \pm 3$

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.

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$