b^2-11b=-15

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Solution for b^2-11b=-15 equation:


Simplifying
b2 + -11b = -15

Reorder the terms:
-11b + b2 = -15

Solving
-11b + b2 = -15

Solving for variable 'b'.

Reorder the terms:
15 + -11b + b2 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -11b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -11b + -15 + b2 = 0 + -15

Reorder the terms:
15 + -15 + -11b + b2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -11b + b2 = 0 + -15
-11b + b2 = 0 + -15

Combine like terms: 0 + -15 = -15
-11b + b2 = -15

The b term is -11b.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11b + 30.25 + b2 = -15 + 30.25

Reorder the terms:
30.25 + -11b + b2 = -15 + 30.25

Combine like terms: -15 + 30.25 = 15.25
30.25 + -11b + b2 = 15.25

Factor a perfect square on the left side:
(b + -5.5)(b + -5.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(b + -5.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

b + -5.5 = 3.905124838 Simplifying b + -5.5 = 3.905124838 Reorder the terms: -5.5 + b = 3.905124838 Solving -5.5 + b = 3.905124838 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = 3.905124838 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = 3.905124838 + 5.5 b = 3.905124838 + 5.5 Combine like terms: 3.905124838 + 5.5 = 9.405124838 b = 9.405124838 Simplifying b = 9.405124838

Subproblem 2

b + -5.5 = -3.905124838 Simplifying b + -5.5 = -3.905124838 Reorder the terms: -5.5 + b = -3.905124838 Solving -5.5 + b = -3.905124838 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + b = -3.905124838 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + b = -3.905124838 + 5.5 b = -3.905124838 + 5.5 Combine like terms: -3.905124838 + 5.5 = 1.594875162 b = 1.594875162 Simplifying b = 1.594875162

Solution

The solution to the problem is based on the solutions from the subproblems. b = {9.405124838, 1.594875162}

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