256x^4=1

Solution for 256x^4=1 equation:

Simplifying
256x4 = 1

Solving
256x4 = 1

Solving for variable 'x'.

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

Divide each side by '256'.
x4 = 0.00390625

Simplifying
x4 = 0.00390625

Reorder the terms:
-0.00390625 + x4 = 0.00390625 + -0.00390625

Combine like terms: 0.00390625 + -0.00390625 = 0.00000000
-0.00390625 + x4 = 0.00000000

Factor a difference between two squares.
(0.0625 + x2)(-0.0625 + x2) = 0.00000000

Factor a difference between two squares.
(0.0625 + x2)((0.25 + x)(-0.25 + x)) = 0.00000000

Subproblem 1
Set the factor '(0.0625 + x2)' equal to zero and attempt to solve:

Simplifying
0.0625 + x2 = 0

Solving
0.0625 + x2 = 0

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

Add '-0.0625' to each side of the equation.
0.0625 + -0.0625 + x2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + x2 = 0 + -0.0625
x2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
x2 = -0.0625

Simplifying
x2 = -0.0625

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 '(0.25 + x)' equal to zero and attempt to solve:

Simplifying
0.25 + x = 0

Solving
0.25 + x = 0

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 0 + -0.25
x = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
x = -0.25

Simplifying
x = -0.25
Subproblem 3
Set the factor '(-0.25 + x)' equal to zero and attempt to solve:

Simplifying
-0.25 + x = 0

Solving
-0.25 + x = 0

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0 + 0.25
x = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
x = 0.25

Simplifying
x = 0.25
Solution
x = {-0.25, 0.25}