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

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

Simplifying
5x4 + x2 + -8 = 0

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

Solving
-8 + x2 + 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 + 0.2x2 + x4 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.2x2 + 1.6 + x4 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.2x2 + x4 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.2x2 + x4 = 0 + 1.6
0.2x2 + x4 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.2x2 + x4 = 1.6

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.2x2 + 0.25 + x4 = 1.6 + 0.25

Reorder the terms:
0.25 + 0.2x2 + x4 = 1.6 + 0.25

Combine like terms: 1.6 + 0.25 = 1.85
0.25 + 0.2x2 + x4 = 1.85

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = 1.85

Calculate the square root of the right side: 1.360147051

Break this problem into two subproblems by setting 
(x2 + 0.5) equal to 1.360147051 and -1.360147051.

Subproblem 1
x2 + 0.5 = 1.360147051

Simplifying
x2 + 0.5 = 1.360147051

Reorder the terms:
0.5 + x2 = 1.360147051

Solving
0.5 + x2 = 1.360147051

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = 1.360147051 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = 1.360147051 + -0.5
x2 = 1.360147051 + -0.5

Combine like terms: 1.360147051 + -0.5 = 0.860147051
x2 = 0.860147051

Simplifying
x2 = 0.860147051

Take the square root of each side:
x = {-0.927441131, 0.927441131}

Subproblem 2
x2 + 0.5 = -1.360147051

Simplifying
x2 + 0.5 = -1.360147051

Reorder the terms:
0.5 + x2 = -1.360147051

Solving
0.5 + x2 = -1.360147051

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x2 = -1.360147051 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x2 = -1.360147051 + -0.5
x2 = -1.360147051 + -0.5

Combine like terms: -1.360147051 + -0.5 = -1.860147051
x2 = -1.860147051

Simplifying
x2 = -1.860147051

Reorder the terms:
1.860147051 + x2 = -1.860147051 + 1.860147051

Combine like terms: -1.860147051 + 1.860147051 = 0.000000000
1.860147051 + 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.