Solve for x (x+8)^4=16

${(x + 8)}^{4} = 16$

Step 1

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

$x + 8 = \pm \sqrt[4]{16}$

Step 2

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

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

$x + 8 = \pm \sqrt[4]{2^{4}}$

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

$x + 8 = \pm 2$

Step 3

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.

$x + 8 = 2$

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

Subtract $8$ from both sides of the equation.

$x = 2 - 8$

Subtract $8$ from $2$ .

$x = - 6$

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

$x + 8 = - 2$

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

Subtract $8$ from both sides of the equation.

$x = - 2 - 8$

Subtract $8$ from $- 2$ .

$x = - 10$

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

$x = - 6, - 10$