x^4=a^4

Solution for x^4=a^4 equation:

Simplifying
x4 = a4

Solving
x4 = a4

Solving for variable 'x'.

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

Simplifying
x4 = a4

Reorder the terms:
-1a4 + x4 = a4 + -1a4

Combine like terms: a4 + -1a4 = 0
-1a4 + x4 = 0

Factor a difference between two squares.
(a2 + x2)(-1a2 + x2) = 0

Factor a difference between two squares.
(a2 + x2)((a + x)(-1a + x)) = 0

Subproblem 1
Set the factor '(a2 + x2)' equal to zero and attempt to solve:

Simplifying
a2 + x2 = 0

Solving
a2 + x2 = 0

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

Add '-1a2' to each side of the equation.
a2 + -1a2 + x2 = 0 + -1a2

Combine like terms: a2 + -1a2 = 0
0 + x2 = 0 + -1a2
x2 = 0 + -1a2
Remove the zero:
x2 = -1a2

Simplifying
x2 = -1a2

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

Simplifying
a + x = 0

Solving
a + x = 0

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

Add '-1a' to each side of the equation.
a + -1a + x = 0 + -1a

Combine like terms: a + -1a = 0
0 + x = 0 + -1a
x = 0 + -1a
Remove the zero:
x = -1a

Simplifying
x = -1a
Subproblem 3
Set the factor '(-1a + x)' equal to zero and attempt to solve:

Simplifying
-1a + x = 0

Solving
-1a + x = 0

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

Add 'a' to each side of the equation.
-1a + a + x = 0 + a

Combine like terms: -1a + a = 0
0 + x = 0 + a
x = 0 + a
Remove the zero:
x = a

Simplifying
x = a
Solution
x = {-1a, a}