1-4r^4=0

Solution for 1-4r^4=0 equation:

Simplifying
1 + -4r4 = 0

Solving
1 + -4r4 = 0

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + -1 + -4r4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r4 = 0 + -1
-4r4 = 0 + -1

Combine like terms: 0 + -1 = -1
-4r4 = -1

Divide each side by '-4'.
r4 = 0.25

Simplifying
r4 = 0.25

Reorder the terms:
-0.25 + r4 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + r4 = 0.00

Factor a difference between two squares.
(0.5 + r2)(-0.5 + r2) = 0.00

Subproblem 1
Set the factor '(0.5 + r2)' equal to zero and attempt to solve:

Simplifying
0.5 + r2 = 0

Solving
0.5 + r2 = 0

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r2 = 0 + -0.5
r2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
r2 = -0.5

Simplifying
r2 = -0.5

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 '(-0.5 + r2)' equal to zero and attempt to solve:

Simplifying
-0.5 + r2 = 0

Solving
-0.5 + r2 = 0

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + r2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r2 = 0 + 0.5
r2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
r2 = 0.5

Simplifying
r2 = 0.5

Take the square root of each side:
r = {-0.707106781, 0.707106781}
Solution
r = {-0.707106781, 0.707106781}