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

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

Simplifying
2x4 + 4x2 + -1 = 0

Reorder the terms:
-1 + 4x2 + 2x4 = 0

Solving
-1 + 4x2 + 2x4 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-0.5 + 2x2 + x4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 2x2 + 0.5 + x4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 2x2 + x4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 2x2 + x4 = 0 + 0.5
2x2 + x4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
2x2 + x4 = 0.5

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = 0.5 + 1

Reorder the terms:
1 + 2x2 + x4 = 0.5 + 1

Combine like terms: 0.5 + 1 = 1.5
1 + 2x2 + x4 = 1.5

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x2 + 1) equal to 1.224744871 and -1.224744871.

Subproblem 1
x2 + 1 = 1.224744871

Simplifying
x2 + 1 = 1.224744871

Reorder the terms:
1 + x2 = 1.224744871

Solving
1 + x2 = 1.224744871

Solving for variable 'x'.

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 = 1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 1.224744871 + -1
x2 = 1.224744871 + -1

Combine like terms: 1.224744871 + -1 = 0.224744871
x2 = 0.224744871

Simplifying
x2 = 0.224744871

Take the square root of each side:
x = {-0.474072643, 0.474072643}

Subproblem 2
x2 + 1 = -1.224744871

Simplifying
x2 + 1 = -1.224744871

Reorder the terms:
1 + x2 = -1.224744871

Solving
1 + x2 = -1.224744871

Solving for variable 'x'.

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 = -1.224744871 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = -1.224744871 + -1
x2 = -1.224744871 + -1

Combine like terms: -1.224744871 + -1 = -2.224744871
x2 = -2.224744871

Simplifying
x2 = -2.224744871

Reorder the terms:
2.224744871 + x2 = -2.224744871 + 2.224744871

Combine like terms: -2.224744871 + 2.224744871 = 0.000000000
2.224744871 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.