x^4-8x^2+0.5=2

Solution for x^4-8x^2+0.5=2 equation:

Simplifying
x4 + -8x2 + 0.5 = 2

Reorder the terms:
0.5 + -8x2 + x4 = 2

Solving
0.5 + -8x2 + x4 = 2

Solving for variable 'x'.

Reorder the terms:
0.5 + -2 + -8x2 + x4 = 2 + -2

Combine like terms: 0.5 + -2 = -1.5
-1.5 + -8x2 + x4 = 2 + -2

Combine like terms: 2 + -2 = 0
-1.5 + -8x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -8x2 + 1.5 + x4 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -8x2 + x4 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -8x2 + x4 = 0 + 1.5
-8x2 + x4 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-8x2 + x4 = 1.5

The x term is -8x2.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x2 + 16 + x4 = 1.5 + 16

Reorder the terms:
16 + -8x2 + x4 = 1.5 + 16

Combine like terms: 1.5 + 16 = 17.5
16 + -8x2 + x4 = 17.5

Factor a perfect square on the left side:
(x2 + -4)(x2 + -4) = 17.5

Calculate the square root of the right side: 4.183300133

Break this problem into two subproblems by setting 
(x2 + -4) equal to 4.183300133 and -4.183300133.

Subproblem 1
x2 + -4 = 4.183300133

Simplifying
x2 + -4 = 4.183300133

Reorder the terms:
-4 + x2 = 4.183300133

Solving
-4 + x2 = 4.183300133

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = 4.183300133 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = 4.183300133 + 4
x2 = 4.183300133 + 4

Combine like terms: 4.183300133 + 4 = 8.183300133
x2 = 8.183300133

Simplifying
x2 = 8.183300133

Take the square root of each side:
x = {-2.860646803, 2.860646803}

Subproblem 2
x2 + -4 = -4.183300133

Simplifying
x2 + -4 = -4.183300133

Reorder the terms:
-4 + x2 = -4.183300133

Solving
-4 + x2 = -4.183300133

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x2 = -4.183300133 + 4

Combine like terms: -4 + 4 = 0
0 + x2 = -4.183300133 + 4
x2 = -4.183300133 + 4

Combine like terms: -4.183300133 + 4 = -0.183300133
x2 = -0.183300133

Simplifying
x2 = -0.183300133

Reorder the terms:
0.183300133 + x2 = -0.183300133 + 0.183300133

Combine like terms: -0.183300133 + 0.183300133 = 0.000000000
0.183300133 + 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.