4x^4-625=0

Solution for 4x^4-625=0 equation:

Simplifying
4x4 + -625 = 0

Reorder the terms:
-625 + 4x4 = 0

Solving
-625 + 4x4 = 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 + 4x4 = 0 + 625

Combine like terms: -625 + 625 = 0
0 + 4x4 = 0 + 625
4x4 = 0 + 625

Combine like terms: 0 + 625 = 625
4x4 = 625

Divide each side by '4'.
x4 = 156.25

Simplifying
x4 = 156.25

Reorder the terms:
-156.25 + x4 = 156.25 + -156.25

Combine like terms: 156.25 + -156.25 = 0.00
-156.25 + x4 = 0.00

Factor a difference between two squares.
(12.5 + x2)(-12.5 + x2) = 0.00

Subproblem 1
Set the factor '(12.5 + x2)' equal to zero and attempt to solve:

Simplifying
12.5 + x2 = 0

Solving
12.5 + x2 = 0

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x2 = 0 + -12.5
x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
x2 = -12.5

Simplifying
x2 = -12.5

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 '(-12.5 + x2)' equal to zero and attempt to solve:

Simplifying
-12.5 + x2 = 0

Solving
-12.5 + x2 = 0

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = 0 + 12.5
x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
x2 = 12.5

Simplifying
x2 = 12.5

Take the square root of each side:
x = {-3.535533906, 3.535533906}
Solution
x = {-3.535533906, 3.535533906}