Find the Roots (Zeros) (x-5)^4=256

${(x - 5)}^{4} = 256$

Step 1

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

$x - 5 = \pm \sqrt[4]{256}$

Step 2

Simplify $\pm \sqrt[4]{256}$ .

Rewrite $256$ as $4^{4}$ .

$x - 5 = \pm \sqrt[4]{4^{4}}$

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

$x - 5 = \pm 4$

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.

$x - 5 = 4$

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

Add $5$ to both sides of the equation.

$x = 4 + 5$

Add $4$ and $5$ .

$x = 9$

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

$x - 5 = - 4$

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

Add $5$ to both sides of the equation.

$x = - 4 + 5$

Add $- 4$ and $5$ .

$x = 1$

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

$x = 9, 1$

Step 4