2x^2=x^4+1

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

Simplifying
2x2 = x4 + 1

Reorder the terms:
2x2 = 1 + x4

Solving
2x2 = 1 + x4

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(-1 + x2)(1 + -1x2) = 0

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

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

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