x^4-22x^2+120=0

Solution for x^4-22x^2+120=0 equation:

Simplifying
x4 + -22x2 + 120 = 0

Reorder the terms:
120 + -22x2 + x4 = 0

Solving
120 + -22x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + -1x2)(12 + -1x2) = 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

Take the square root of each side:
x = {-3.16227766, 3.16227766}
Subproblem 2
Set the factor '(12 + -1x2)' equal to zero and attempt to solve:

Simplifying
12 + -1x2 = 0

Solving
12 + -1x2 = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x2 = 0 + -12
-1x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1x2 = -12

Divide each side by '-1'.
x2 = 12

Simplifying
x2 = 12

Take the square root of each side:
x = {-3.464101615, 3.464101615}
Solution
x = {-3.16227766, 3.16227766, -3.464101615, 3.464101615}