x^4-625=0

Solution for x^4-625=0 equation:

Simplifying
x4 + -625 = 0

Reorder the terms:
-625 + x4 = 0

Solving
-625 + x4 = 0

Solving for variable 'x'.

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

Add '625' to each side of the equation.
-625 + 625 + x4 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + x4 = 0 + 625
x4 = 0 + 625

Combine like terms: 0 + 625 = 625
x4 = 625

Simplifying
x4 = 625

Reorder the terms:
-625 + x4 = 625 + -625

Combine like terms: 625 + -625 = 0
-625 + x4 = 0

Factor a difference between two squares.
(25 + x2)(-25 + x2) = 0

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

Subproblem 1
Set the factor '(25 + x2)' equal to zero and attempt to solve:

Simplifying
25 + x2 = 0

Solving
25 + x2 = 0

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

Add '-25' to each side of the equation.
25 + -25 + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x2 = 0 + -25
x2 = 0 + -25

Combine like terms: 0 + -25 = -25
x2 = -25

Simplifying
x2 = -25

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 + 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 + 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
Solution
x = {-5, 5}