15b-b^2=36.25

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Solution for 15b-b^2=36.25 equation:


Simplifying
15b + -1b2 = 36.25

Solving
15b + -1b2 = 36.25

Solving for variable 'b'.

Reorder the terms:
-36.25 + 15b + -1b2 = 36.25 + -36.25

Combine like terms: 36.25 + -36.25 = 0.00
-36.25 + 15b + -1b2 = 0.00

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

Divide each side by '-1'.
36.25 + -15b + b2 = 0.00

Move the constant term to the right:

Add '-36.25' to each side of the equation.
36.25 + -15b + -36.25 + b2 = 0.00 + -36.25

Reorder the terms:
36.25 + -36.25 + -15b + b2 = 0.00 + -36.25

Combine like terms: 36.25 + -36.25 = 0.00
0.00 + -15b + b2 = 0.00 + -36.25
-15b + b2 = 0.00 + -36.25

Combine like terms: 0.00 + -36.25 = -36.25
-15b + b2 = -36.25

The b term is -15b.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15b + 56.25 + b2 = -36.25 + 56.25

Reorder the terms:
56.25 + -15b + b2 = -36.25 + 56.25

Combine like terms: -36.25 + 56.25 = 20
56.25 + -15b + b2 = 20

Factor a perfect square on the left side:
(b + -7.5)(b + -7.5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(b + -7.5) equal to 4.472135955 and -4.472135955.

Subproblem 1

b + -7.5 = 4.472135955 Simplifying b + -7.5 = 4.472135955 Reorder the terms: -7.5 + b = 4.472135955 Solving -7.5 + b = 4.472135955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + b = 4.472135955 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + b = 4.472135955 + 7.5 b = 4.472135955 + 7.5 Combine like terms: 4.472135955 + 7.5 = 11.972135955 b = 11.972135955 Simplifying b = 11.972135955

Subproblem 2

b + -7.5 = -4.472135955 Simplifying b + -7.5 = -4.472135955 Reorder the terms: -7.5 + b = -4.472135955 Solving -7.5 + b = -4.472135955 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + b = -4.472135955 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + b = -4.472135955 + 7.5 b = -4.472135955 + 7.5 Combine like terms: -4.472135955 + 7.5 = 3.027864045 b = 3.027864045 Simplifying b = 3.027864045

Solution

The solution to the problem is based on the solutions from the subproblems. b = {11.972135955, 3.027864045}

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