3.14*b-b^2=2.25

Solution for 3.14*b-b^2=2.25 equation:

Simplifying
3.14b + -1b2 = 2.25

Solving
3.14b + -1b2 = 2.25

Solving for variable 'b'.

Reorder the terms:
-2.25 + 3.14b + -1b2 = 2.25 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
-2.25 + 3.14b + -1b2 = 0.00

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

Divide each side by '-1'.
2.25 + -3.14b + b2 = 0.00

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -3.14b + -2.25 + b2 = 0.00 + -2.25

Reorder the terms:
2.25 + -2.25 + -3.14b + b2 = 0.00 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -3.14b + b2 = 0.00 + -2.25
-3.14b + b2 = 0.00 + -2.25

Combine like terms: 0.00 + -2.25 = -2.25
-3.14b + b2 = -2.25

The b term is -3.14b.  Take half its coefficient (-1.57).
Square it (2.4649) and add it to both sides.

Add '2.4649' to each side of the equation.
-3.14b + 2.4649 + b2 = -2.25 + 2.4649

Reorder the terms:
2.4649 + -3.14b + b2 = -2.25 + 2.4649

Combine like terms: -2.25 + 2.4649 = 0.2149
2.4649 + -3.14b + b2 = 0.2149

Factor a perfect square on the left side:
(b + -1.57)(b + -1.57) = 0.2149

Calculate the square root of the right side: 0.463573079

Break this problem into two subproblems by setting 
(b + -1.57) equal to 0.463573079 and -0.463573079.

Subproblem 1
b + -1.57 = 0.463573079

Simplifying
b + -1.57 = 0.463573079

Reorder the terms:
-1.57 + b = 0.463573079

Solving
-1.57 + b = 0.463573079

Solving for variable 'b'.

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

Add '1.57' to each side of the equation.
-1.57 + 1.57 + b = 0.463573079 + 1.57

Combine like terms: -1.57 + 1.57 = 0.00
0.00 + b = 0.463573079 + 1.57
b = 0.463573079 + 1.57

Combine like terms: 0.463573079 + 1.57 = 2.033573079
b = 2.033573079

Simplifying
b = 2.033573079

Subproblem 2
b + -1.57 = -0.463573079

Simplifying
b + -1.57 = -0.463573079

Reorder the terms:
-1.57 + b = -0.463573079

Solving
-1.57 + b = -0.463573079

Solving for variable 'b'.

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

Add '1.57' to each side of the equation.
-1.57 + 1.57 + b = -0.463573079 + 1.57

Combine like terms: -1.57 + 1.57 = 0.00
0.00 + b = -0.463573079 + 1.57
b = -0.463573079 + 1.57

Combine like terms: -0.463573079 + 1.57 = 1.106426921
b = 1.106426921

Simplifying
b = 1.106426921

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.033573079, 1.106426921}