x^4+8x^2-90=0

Solution for x^4+8x^2-90=0 equation:

Simplifying
x4 + 8x2 + -90 = 0

Reorder the terms:
-90 + 8x2 + x4 = 0

Solving
-90 + 8x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 8x2 + 90 + x4 = 0 + 90

Reorder the terms:
-90 + 90 + 8x2 + x4 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 8x2 + x4 = 0 + 90
8x2 + x4 = 0 + 90

Combine like terms: 0 + 90 = 90
8x2 + x4 = 90

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 = 90 + 16

Reorder the terms:
16 + 8x2 + x4 = 90 + 16

Combine like terms: 90 + 16 = 106
16 + 8x2 + x4 = 106

Factor a perfect square on the left side:
(x2 + 4)(x2 + 4) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x2 + 4) equal to 10.295630141 and -10.295630141.

Subproblem 1
x2 + 4 = 10.295630141

Simplifying
x2 + 4 = 10.295630141

Reorder the terms:
4 + x2 = 10.295630141

Solving
4 + x2 = 10.295630141

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 = 10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = 10.295630141 + -4
x2 = 10.295630141 + -4

Combine like terms: 10.295630141 + -4 = 6.295630141
x2 = 6.295630141

Simplifying
x2 = 6.295630141

Take the square root of each side:
x = {-2.509109432, 2.509109432}

Subproblem 2
x2 + 4 = -10.295630141

Simplifying
x2 + 4 = -10.295630141

Reorder the terms:
4 + x2 = -10.295630141

Solving
4 + x2 = -10.295630141

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 = -10.295630141 + -4

Combine like terms: 4 + -4 = 0
0 + x2 = -10.295630141 + -4
x2 = -10.295630141 + -4

Combine like terms: -10.295630141 + -4 = -14.295630141
x2 = -14.295630141

Simplifying
x2 = -14.295630141

Reorder the terms:
14.295630141 + x2 = -14.295630141 + 14.295630141

Combine like terms: -14.295630141 + 14.295630141 = 0.000000000
14.295630141 + 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.