5b^2-5b+1=0

Solution for 5b^2-5b+1=0 equation:

Simplifying
5b2 + -5b + 1 = 0

Reorder the terms:
1 + -5b + 5b2 = 0

Solving
1 + -5b + 5b2 = 0

Solving for variable 'b'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.2 + -1b + b2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -1b + -0.2 + b2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -1b + b2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -1b + b2 = 0 + -0.2
-1b + b2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-1b + b2 = -0.2

The b term is -1b.  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.
-1b + 0.25 + b2 = -0.2 + 0.25

Reorder the terms:
0.25 + -1b + b2 = -0.2 + 0.25

Combine like terms: -0.2 + 0.25 = 0.05
0.25 + -1b + b2 = 0.05

Factor a perfect square on the left side:
(b + -0.5)(b + -0.5) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(b + -0.5) equal to 0.223606798 and -0.223606798.

Subproblem 1
b + -0.5 = 0.223606798

Simplifying
b + -0.5 = 0.223606798

Reorder the terms:
-0.5 + b = 0.223606798

Solving
-0.5 + b = 0.223606798

Solving for variable 'b'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + b = 0.223606798 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b = 0.223606798 + 0.5
b = 0.223606798 + 0.5

Combine like terms: 0.223606798 + 0.5 = 0.723606798
b = 0.723606798

Simplifying
b = 0.723606798

Subproblem 2
b + -0.5 = -0.223606798

Simplifying
b + -0.5 = -0.223606798

Reorder the terms:
-0.5 + b = -0.223606798

Solving
-0.5 + b = -0.223606798

Solving for variable 'b'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + b = -0.223606798 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + b = -0.223606798 + 0.5
b = -0.223606798 + 0.5

Combine like terms: -0.223606798 + 0.5 = 0.276393202
b = 0.276393202

Simplifying
b = 0.276393202

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.723606798, 0.276393202}