x^4-2x^2=2

Solution for x^4-2x^2=2 equation:

Simplifying
x4 + -2x2 = 2

Reorder the terms:
-2x2 + x4 = 2

Solving
-2x2 + x4 = 2

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + -2x2 + x4 = 3

Factor a perfect square on the left side:
(x2 + -1)(x2 + -1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x2 + -1) equal to 1.732050808 and -1.732050808.

Subproblem 1
x2 + -1 = 1.732050808

Simplifying
x2 + -1 = 1.732050808

Reorder the terms:
-1 + x2 = 1.732050808

Solving
-1 + x2 = 1.732050808

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 = 1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = 1.732050808 + 1
x2 = 1.732050808 + 1

Combine like terms: 1.732050808 + 1 = 2.732050808
x2 = 2.732050808

Simplifying
x2 = 2.732050808

Take the square root of each side:
x = {-1.65289165, 1.65289165}

Subproblem 2
x2 + -1 = -1.732050808

Simplifying
x2 + -1 = -1.732050808

Reorder the terms:
-1 + x2 = -1.732050808

Solving
-1 + x2 = -1.732050808

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 = -1.732050808 + 1

Combine like terms: -1 + 1 = 0
0 + x2 = -1.732050808 + 1
x2 = -1.732050808 + 1

Combine like terms: -1.732050808 + 1 = -0.732050808
x2 = -0.732050808

Simplifying
x2 = -0.732050808

Reorder the terms:
0.732050808 + x2 = -0.732050808 + 0.732050808

Combine like terms: -0.732050808 + 0.732050808 = 0.000000000
0.732050808 + 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.