2x^4-5x^2-2=0

Solution for 2x^4-5x^2-2=0 equation:

Simplifying
2x4 + -5x2 + -2 = 0

Reorder the terms:
-2 + -5x2 + 2x4 = 0

Solving
-2 + -5x2 + 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'.
-1 + -2.5x2 + x4 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.5x2 + 1 + x4 = 0 + 1

Reorder the terms:
-1 + 1 + -2.5x2 + x4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.5x2 + x4 = 0 + 1
-2.5x2 + x4 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.5x2 + x4 = 1

The x term is -2.5x2.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x2 + 1.5625 + x4 = 1 + 1.5625

Reorder the terms:
1.5625 + -2.5x2 + x4 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + -2.5x2 + x4 = 2.5625

Factor a perfect square on the left side:
(x2 + -1.25)(x2 + -1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x2 + -1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
x2 + -1.25 = 1.600781059

Simplifying
x2 + -1.25 = 1.600781059

Reorder the terms:
-1.25 + x2 = 1.600781059

Solving
-1.25 + x2 = 1.600781059

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x2 = 1.600781059 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x2 = 1.600781059 + 1.25
x2 = 1.600781059 + 1.25

Combine like terms: 1.600781059 + 1.25 = 2.850781059
x2 = 2.850781059

Simplifying
x2 = 2.850781059

Take the square root of each side:
x = {-1.688425615, 1.688425615}

Subproblem 2
x2 + -1.25 = -1.600781059

Simplifying
x2 + -1.25 = -1.600781059

Reorder the terms:
-1.25 + x2 = -1.600781059

Solving
-1.25 + x2 = -1.600781059

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x2 = -1.600781059 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x2 = -1.600781059 + 1.25
x2 = -1.600781059 + 1.25

Combine like terms: -1.600781059 + 1.25 = -0.350781059
x2 = -0.350781059

Simplifying
x2 = -0.350781059

Reorder the terms:
0.350781059 + x2 = -0.350781059 + 0.350781059

Combine like terms: -0.350781059 + 0.350781059 = 0.000000000
0.350781059 + 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.