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 = 45.16
25 + -10b + b2 = 45.16

Factor a perfect square on the left side:
(b + -5)(b + -5) = 45.16

Calculate the square root of the right side: 6.720119047

Break this problem into two subproblems by setting 
(b + -5) equal to 6.720119047 and -6.720119047.

Subproblem 1

b + -5 = 6.720119047 Simplifying b + -5 = 6.720119047 Reorder the terms: -5 + b = 6.720119047 Solving -5 + b = 6.720119047 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 = 6.720119047 + 5 Combine like terms: -5 + 5 = 0 0 + b = 6.720119047 + 5 b = 6.720119047 + 5 Combine like terms: 6.720119047 + 5 = 11.720119047 b = 11.720119047 Simplifying b = 11.720119047

Subproblem 2

b + -5 = -6.720119047 Simplifying b + -5 = -6.720119047 Reorder the terms: -5 + b = -6.720119047 Solving -5 + b = -6.720119047 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 = -6.720119047 + 5 Combine like terms: -5 + 5 = 0 0 + b = -6.720119047 + 5 b = -6.720119047 + 5 Combine like terms: -6.720119047 + 5 = -1.720119047 b = -1.720119047 Simplifying b = -1.720119047

Solution

The solution to the problem is based on the solutions from the subproblems. b = {11.720119047, -1.720119047}

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