X^4+1=x^4+2x^2+1-2x^2

Solution for X^4+1=x^4+2x^2+1-2x^2 equation:

Simplifying
X4 + 1 = x4 + 2x2 + 1 + -2x2

Reorder the terms:
1 + X4 = x4 + 2x2 + 1 + -2x2

Reorder the terms:
1 + X4 = 1 + 2x2 + -2x2 + x4

Combine like terms: 2x2 + -2x2 = 0
1 + X4 = 1 + 0 + x4
1 + X4 = 1 + x4

Add '-1' to each side of the equation.
1 + -1 + X4 = 1 + -1 + x4

Combine like terms: 1 + -1 = 0
0 + X4 = 1 + -1 + x4
X4 = 1 + -1 + x4

Combine like terms: 1 + -1 = 0
X4 = 0 + x4
X4 = x4

Solving
X4 = x4

Solving for variable 'X'.

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

Simplifying
X4 = x4

Combine like terms: x4 + -1x4 = 0
X4 + -1x4 = 0

Factor a difference between two squares.
(X2 + x2)(X2 + -1x2) = 0

Factor a difference between two squares.
(X2 + x2)((X + x)(X + -1x)) = 0

Subproblem 1
Set the factor '(X2 + x2)' equal to zero and attempt to solve:

Simplifying
X2 + x2 = 0

Solving
X2 + x2 = 0

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

Add '-1x2' to each side of the equation.
X2 + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
X2 + 0 = 0 + -1x2
X2 = 0 + -1x2
Remove the zero:
X2 = -1x2

Simplifying
X2 = -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 '(X + x)' equal to zero and attempt to solve:

Simplifying
X + x = 0

Solving
X + x = 0

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

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

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

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

Simplifying
X + -1x = 0

Solving
X + -1x = 0

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

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

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

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