5x^4-125=0

Solution for 5x^4-125=0 equation:

Simplifying
5x4 + -125 = 0

Reorder the terms:
-125 + 5x4 = 0

Solving
-125 + 5x4 = 0

Solving for variable 'x'.

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

Add '125' to each side of the equation.
-125 + 125 + 5x4 = 0 + 125

Combine like terms: -125 + 125 = 0
0 + 5x4 = 0 + 125
5x4 = 0 + 125

Combine like terms: 0 + 125 = 125
5x4 = 125

Divide each side by '5'.
x4 = 25

Simplifying
x4 = 25

Reorder the terms:
-25 + x4 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + x4 = 0

Factor a difference between two squares.
(5 + x2)(-5 + x2) = 0

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

Simplifying
5 + x2 = 0

Solving
5 + x2 = 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 + x2 = 0 + -5

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

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

Simplifying
x2 = -5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-5 + x2)' equal to zero and attempt to solve:

Simplifying
-5 + x2 = 0

Solving
-5 + x2 = 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 + x2 = 0 + 5

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

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

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-2.236067978, 2.236067978}