Solve for x x^4+19=100

$x^{4} + 19 = 100$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Subtract $19$ from both sides of the equation.

$x^{4} = 100 - 19$

Subtract $19$ from $100$ .

$x^{4} = 81$

Step 2

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

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

Step 3

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 4

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.

$x = 3, - 3$