(x^4)-(30x^2)+125=0

Solution for (x^4)-(30x^2)+125=0 equation:

Simplifying
(x4) + -1(30x2) + 125 = 0
x4 + -1(30x2) + 125 = 0

Remove parenthesis around (30x2)
x4 + -1 * 30x2 + 125 = 0

Multiply -1 * 30
x4 + -30x2 + 125 = 0

Reorder the terms:
125 + -30x2 + x4 = 0

Solving
125 + -30x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x2)(25 + -1x2) = 0

Factor a difference between two squares.
(5 + -1x2)((5 + x)(5 + -1x)) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

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

Simplifying
x = 5
Solution
x = {-2.236067978, 2.236067978, -5, 5}