0=x^4-x^2-20

Solution for 0=x^4-x^2-20 equation:

Simplifying
0 = x4 + -1x2 + -20

Reorder the terms:
0 = -20 + -1x2 + x4

Solving
0 = -20 + -1x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + x2 + -1x4 = -20 + -1x2 + x4 + 20 + x2 + -1x4

Reorder the terms:
20 + x2 + -1x4 = -20 + 20 + -1x2 + x2 + x4 + -1x4

Combine like terms: -20 + 20 = 0
20 + x2 + -1x4 = 0 + -1x2 + x2 + x4 + -1x4
20 + x2 + -1x4 = -1x2 + x2 + x4 + -1x4

Combine like terms: -1x2 + x2 = 0
20 + x2 + -1x4 = 0 + x4 + -1x4
20 + x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
20 + x2 + -1x4 = 0

Factor a trinomial.
(5 + -1x2)(4 + x2) = 0

Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(4 + x2)' equal to zero and attempt to solve:

Simplifying
4 + x2 = 0

Solving
4 + x2 = 0

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 = 0 + -4

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

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

Simplifying
x2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.236067978, 2.236067978}