x^4-22x^2+117=0

Solution for x^4-22x^2+117=0 equation:

Simplifying
x4 + -22x2 + 117 = 0

Reorder the terms:
117 + -22x2 + x4 = 0

Solving
117 + -22x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -1x2)(13 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(3 + -1x))(13 + -1x2) = 0

Subproblem 1
Set the factor '(13 + -1x2)' equal to zero and attempt to solve:

Simplifying
13 + -1x2 = 0

Solving
13 + -1x2 = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x2 = 0 + -13
-1x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-1x2 = -13

Divide each side by '-1'.
x2 = 13

Simplifying
x2 = 13

Take the square root of each side:
x = {-3.605551275, 3.605551275}
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 = {-3.605551275, 3.605551275, -3, 3}