x^4-a^4=0

Solution for x^4-a^4=0 equation:

Simplifying
x4 + -1a4 = 0

Reorder the terms:
-1a4 + x4 = 0

Solving
-1a4 + x4 = 0

Solving for variable 'a'.

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

Add '-1x4' to each side of the equation.
-1a4 + x4 + -1x4 = 0 + -1x4

Combine like terms: x4 + -1x4 = 0
-1a4 + 0 = 0 + -1x4
-1a4 = 0 + -1x4
Remove the zero:
-1a4 = -1x4

Divide each side by '-1'.
a4 = x4

Simplifying
a4 = x4

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

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

Factor a difference between two squares.
(a2 + x2)((a + x)(a + -1x)) = 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 a to the left, all other terms to the right.

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

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

Simplifying
a2 = -1x2

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 a to the left, all other terms to the right.

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

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

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

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

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

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