x^4-256=0

Solution for x^4-256=0 equation:

Simplifying
x4 + -256 = 0

Reorder the terms:
-256 + x4 = 0

Solving
-256 + x4 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '256' to each side of the equation.
-256 + 256 + x4 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + x4 = 0 + 256
x4 = 0 + 256

Combine like terms: 0 + 256 = 256
x4 = 256

Simplifying
x4 = 256

Reorder the terms:
-256 + x4 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + x4 = 0

Factor a difference between two squares.
(16 + x2)(-16 + x2) = 0

Factor a difference between two squares.
(16 + x2)((4 + x)(-4 + x)) = 0

Subproblem 1
Set the factor '(16 + x2)' equal to zero and attempt to solve:

Simplifying
16 + x2 = 0

Solving
16 + x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x2 = 0 + -16
x2 = 0 + -16

Combine like terms: 0 + -16 = -16
x2 = -16

Simplifying
x2 = -16

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 3
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {-4, 4}