Evaluate x^6+36=100

$x^{6} + 36 = 100$

Step 1

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

Subtract $36$ from both sides of the equation.

$x^{6} = 100 - 36$

Subtract $36$ from $100$ .

$x^{6} = 64$

Step 2

Take the 6th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[6]{64}$

Step 3

Simplify $\pm \sqrt[6]{64}$ .

Rewrite $64$ as $2^{6}$ .

$x = \pm \sqrt[6]{2^{6}}$

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

$x = \pm 2$

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.

$x = 2$

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.

$x = 2, - 2$