2b*b-20*b=-40.32

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Solution for 2b*b-20*b=-40.32 equation: 


Simplifying
2b * b + -20b = -40.32

Multiply b * b
2b2 + -20b = -40.32

Reorder the terms:
-20b + 2b2 = -40.32

Solving
-20b + 2b2 = -40.32

Solving for variable 'b'.

Reorder the terms:
40.32 + -20b + 2b2 = -40.32 + 40.32

Combine like terms: -40.32 + 40.32 = 0.00
40.32 + -20b + 2b2 = 0.00

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

Divide each side by '2'.
20.16 + -10b + b2 = 0.00

Move the constant term to the right:

Add '-20.16' to each side of the equation.
20.16 + -10b + -20.16 + b2 = 0.00 + -20.16

Reorder the terms:
20.16 + -20.16 + -10b + b2 = 0.00 + -20.16

Combine like terms: 20.16 + -20.16 = 0.00
0.00 + -10b + b2 = 0.00 + -20.16
-10b + b2 = 0.00 + -20.16

Combine like terms: 0.00 + -20.16 = -20.16
-10b + b2 = -20.16

The b term is -10b.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10b + 25 + b2 = -20.16 + 25

Reorder the terms:
25 + -10b + b2 = -20.16 + 25

Combine like terms: -20.16 + 25 = 4.84
25 + -10b + b2 = 4.84

Factor a perfect square on the left side:
(b + -5)(b + -5) = 4.84

Calculate the square root of the right side: 2.2

Break this problem into two subproblems by setting 
(b + -5) equal to 2.2 and -2.2.


Subproblem 1
b + -5 = 2.2

Simplifying
b + -5 = 2.2

Reorder the terms:
-5 + b = 2.2

Solving
-5 + b = 2.2

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + 5 + b = 2.2 + 5

Combine like terms: -5 + 5 = 0
0 + b = 2.2 + 5
b = 2.2 + 5

Combine like terms: 2.2 + 5 = 7.2
b = 7.2

Simplifying
b = 7.2


Subproblem 2
b + -5 = -2.2

Simplifying
b + -5 = -2.2

Reorder the terms:
-5 + b = -2.2

Solving
-5 + b = -2.2

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + 5 + b = -2.2 + 5

Combine like terms: -5 + 5 = 0
0 + b = -2.2 + 5
b = -2.2 + 5

Combine like terms: -2.2 + 5 = 2.8
b = 2.8

Simplifying
b = 2.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {7.2, 2.8}

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