25k^4-1=0

Solution for 25k^4-1=0 equation:

Simplifying
25k4 + -1 = 0

Reorder the terms:
-1 + 25k4 = 0

Solving
-1 + 25k4 = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + 1 + 25k4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 25k4 = 0 + 1
25k4 = 0 + 1

Combine like terms: 0 + 1 = 1
25k4 = 1

Divide each side by '25'.
k4 = 0.04

Simplifying
k4 = 0.04

Reorder the terms:
-0.04 + k4 = 0.04 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
-0.04 + k4 = 0.00

Factor a difference between two squares.
(0.2 + k2)(-0.2 + k2) = 0.00

Subproblem 1
Set the factor '(0.2 + k2)' equal to zero and attempt to solve:

Simplifying
0.2 + k2 = 0

Solving
0.2 + k2 = 0

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + k2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + k2 = 0 + -0.2
k2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
k2 = -0.2

Simplifying
k2 = -0.2

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 '(-0.2 + k2)' equal to zero and attempt to solve:

Simplifying
-0.2 + k2 = 0

Solving
-0.2 + k2 = 0

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + k2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + k2 = 0 + 0.2
k2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
k2 = 0.2

Simplifying
k2 = 0.2

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