28=b(b-1)

Solution for 28=b(b-1) equation:

Simplifying
28 = b(b + -1)

Reorder the terms:
28 = b(-1 + b)
28 = (-1 * b + b * b)
28 = (-1b + b2)

Solving
28 = -1b + b2

Solving for variable 'b'.

Reorder the terms:
28 + b + -1b2 = -1b + b + b2 + -1b2

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-28 + -1b + b2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -1b + 28 + b2 = 0 + 28

Reorder the terms:
-28 + 28 + -1b + b2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -1b + b2 = 0 + 28
-1b + b2 = 0 + 28

Combine like terms: 0 + 28 = 28
-1b + b2 = 28

The b term is b.  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 = 28 + 0.25

Reorder the terms:
0.25 + -1b + b2 = 28 + 0.25

Combine like terms: 28 + 0.25 = 28.25
0.25 + -1b + b2 = 28.25

Factor a perfect square on the left side:
(b + 0.5)(b + 0.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(b + 0.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
b + 0.5 = 5.315072906

Simplifying
b + 0.5 = 5.315072906

Reorder the terms:
0.5 + b = 5.315072906

Solving
0.5 + b = 5.315072906

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 = 5.315072906 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = 5.315072906 + -0.5
b = 5.315072906 + -0.5

Combine like terms: 5.315072906 + -0.5 = 4.815072906
b = 4.815072906

Simplifying
b = 4.815072906

Subproblem 2
b + 0.5 = -5.315072906

Simplifying
b + 0.5 = -5.315072906

Reorder the terms:
0.5 + b = -5.315072906

Solving
0.5 + b = -5.315072906

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 = -5.315072906 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + b = -5.315072906 + -0.5
b = -5.315072906 + -0.5

Combine like terms: -5.315072906 + -0.5 = -5.815072906
b = -5.815072906

Simplifying
b = -5.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.815072906, -5.815072906}