0=2x^4+x^2-1

Solution for 0=2x^4+x^2-1 equation:

Simplifying
0 = 2x4 + x2 + -1

Reorder the terms:
0 = -1 + x2 + 2x4

Solving
0 = -1 + x2 + 2x4

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(1 + -2x2)(1 + x2) = 0

Subproblem 1
Set the factor '(1 + -2x2)' equal to zero and attempt to solve:

Simplifying
1 + -2x2 = 0

Solving
1 + -2x2 = 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 + -2x2 = 0 + -1

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

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

Divide each side by '-2'.
x2 = 0.5

Simplifying
x2 = 0.5

Take the square root of each side:
x = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(1 + x2)' equal to zero and attempt to solve:

Simplifying
1 + x2 = 0

Solving
1 + x2 = 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 + x2 = 0 + -1

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

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

Simplifying
x2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-0.707106781, 0.707106781}