25x^4-y^4=0

Solution for 25x^4-y^4=0 equation:

Simplifying
25x4 + -1y4 = 0

Solving
25x4 + -1y4 = 0

Solving for variable 'x'.

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

Add 'y4' to each side of the equation.
25x4 + -1y4 + y4 = 0 + y4

Combine like terms: -1y4 + y4 = 0
25x4 + 0 = 0 + y4
25x4 = 0 + y4
Remove the zero:
25x4 = y4

Divide each side by '25'.
x4 = 0.04y4

Simplifying
x4 = 0.04y4

Combine like terms: 0.04y4 + -0.04y4 = 0.00
x4 + -0.04y4 = 0.00

Factor a difference between two squares.
(x2 + 0.2y2)(x2 + -0.2y2) = 0.00

Subproblem 1
Set the factor '(x2 + 0.2y2)' equal to zero and attempt to solve:

Simplifying
x2 + 0.2y2 = 0

Solving
x2 + 0.2y2 = 0

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

Add '-0.2y2' to each side of the equation.
x2 + 0.2y2 + -0.2y2 = 0 + -0.2y2

Combine like terms: 0.2y2 + -0.2y2 = 0.0
x2 + 0.0 = 0 + -0.2y2
x2 = 0 + -0.2y2
Remove the zero:
x2 = -0.2y2

Simplifying
x2 = -0.2y2

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 '(x2 + -0.2y2)' equal to zero and attempt to solve:

Simplifying
x2 + -0.2y2 = 0

Solving
x2 + -0.2y2 = 0

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

Add '0.2y2' to each side of the equation.
x2 + -0.2y2 + 0.2y2 = 0 + 0.2y2

Combine like terms: -0.2y2 + 0.2y2 = 0.0
x2 + 0.0 = 0 + 0.2y2
x2 = 0 + 0.2y2
Remove the zero:
x2 = 0.2y2

Simplifying
x2 = 0.2y2

Take the square root of each side:
x = {-0.447213596y, 0.447213596y}
Solution
x = {-0.447213596y, 0.447213596y}