5x^4-2x^2-8=0

Solution for 5x^4-2x^2-8=0 equation:

Simplifying
5x4 + -2x2 + -8 = 0

Reorder the terms:
-8 + -2x2 + 5x4 = 0

Solving
-8 + -2x2 + 5x4 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-1.6 + -0.4x2 + x4 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.4x2 + 1.6 + x4 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.4x2 + x4 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.4x2 + x4 = 0 + 1.6
-0.4x2 + x4 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.4x2 + x4 = 1.6

The x term is -0.4x2.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x2 + 0.04 + x4 = 1.6 + 0.04

Reorder the terms:
0.04 + -0.4x2 + x4 = 1.6 + 0.04

Combine like terms: 1.6 + 0.04 = 1.64
0.04 + -0.4x2 + x4 = 1.64

Factor a perfect square on the left side:
(x2 + -0.2)(x2 + -0.2) = 1.64

Calculate the square root of the right side: 1.280624847

Break this problem into two subproblems by setting 
(x2 + -0.2) equal to 1.280624847 and -1.280624847.

Subproblem 1
x2 + -0.2 = 1.280624847

Simplifying
x2 + -0.2 = 1.280624847

Reorder the terms:
-0.2 + x2 = 1.280624847

Solving
-0.2 + x2 = 1.280624847

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x2 = 1.280624847 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x2 = 1.280624847 + 0.2
x2 = 1.280624847 + 0.2

Combine like terms: 1.280624847 + 0.2 = 1.480624847
x2 = 1.480624847

Simplifying
x2 = 1.480624847

Take the square root of each side:
x = {-1.216809289, 1.216809289}

Subproblem 2
x2 + -0.2 = -1.280624847

Simplifying
x2 + -0.2 = -1.280624847

Reorder the terms:
-0.2 + x2 = -1.280624847

Solving
-0.2 + x2 = -1.280624847

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x2 = -1.280624847 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x2 = -1.280624847 + 0.2
x2 = -1.280624847 + 0.2

Combine like terms: -1.280624847 + 0.2 = -1.080624847
x2 = -1.080624847

Simplifying
x2 = -1.080624847

Reorder the terms:
1.080624847 + x2 = -1.080624847 + 1.080624847

Combine like terms: -1.080624847 + 1.080624847 = 0.000000000
1.080624847 + 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.