x^4+x^2=90

Solution for x^4+x^2=90 equation:

Simplifying
x4 + x2 = 90

Reorder the terms:
x2 + x4 = 90

Solving
x2 + x4 = 90

Solving for variable 'x'.

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

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

Factor a trinomial.
(-10 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
(-10 + -1x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(-10 + -1x2)' equal to zero and attempt to solve:

Simplifying
-10 + -1x2 = 0

Solving
-10 + -1x2 = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x2 = 0 + 10
-1x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-1x2 = 10

Divide each side by '-1'.
x2 = -10

Simplifying
x2 = -10

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3, 3}