0=x^4+6x^2-55

Solution for 0=x^4+6x^2-55 equation:

Simplifying
0 = x4 + 6x2 + -55

Reorder the terms:
0 = -55 + 6x2 + x4

Solving
0 = -55 + 6x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 55 = 55
55 + -6x2 + -1x4 = -55 + 6x2 + x4 + 55 + -6x2 + -1x4

Reorder the terms:
55 + -6x2 + -1x4 = -55 + 55 + 6x2 + -6x2 + x4 + -1x4

Combine like terms: -55 + 55 = 0
55 + -6x2 + -1x4 = 0 + 6x2 + -6x2 + x4 + -1x4
55 + -6x2 + -1x4 = 6x2 + -6x2 + x4 + -1x4

Combine like terms: 6x2 + -6x2 = 0
55 + -6x2 + -1x4 = 0 + x4 + -1x4
55 + -6x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
55 + -6x2 + -1x4 = 0

Factor a trinomial.
(5 + -1x2)(11 + 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 '(11 + x2)' equal to zero and attempt to solve:

Simplifying
11 + x2 = 0

Solving
11 + x2 = 0

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

Add '-11' to each side of the equation.
11 + -11 + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x2 = 0 + -11
x2 = 0 + -11

Combine like terms: 0 + -11 = -11
x2 = -11

Simplifying
x2 = -11

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}