r^2-r+0.25=0

Solution for r^2-r+0.25=0 equation:

Simplifying
r2 + -1r + 0.25 = 0

Reorder the terms:
0.25 + -1r + r2 = 0

Solving
0.25 + -1r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1r + -0.25 + r2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1r + r2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1r + r2 = 0 + -0.25
-1r + r2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1r + r2 = -0.25

The r term is -1r.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1r + 0.25 + r2 = -0.25 + 0.25

Reorder the terms:
0.25 + -1r + r2 = -0.25 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.25 + -1r + r2 = 0.00

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(r + -0.5) equal to 0.00 and 0.00.

Subproblem 1
r + -0.5 = 0.00

Simplifying
r + -0.5 = 0.00

Reorder the terms:
-0.5 + r = 0.00

Solving
-0.5 + r = 0.00

Solving for variable 'r'.

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 + r = 0.00 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r = 0.00 + 0.5
r = 0.00 + 0.5

Combine like terms: 0.00 + 0.5 = 0.5
r = 0.5

Simplifying
r = 0.5

Subproblem 2
r + -0.5 = 0.00

Simplifying
r + -0.5 = 0.00

Reorder the terms:
-0.5 + r = 0.00

Solving
-0.5 + r = 0.00

Solving for variable 'r'.

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 + r = 0.00 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + r = 0.00 + 0.5
r = 0.00 + 0.5

Combine like terms: 0.00 + 0.5 = 0.5
r = 0.5

Simplifying
r = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.5, 0.5}