(44-b)b=60

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Solution for (44-b)b=60 equation:


Simplifying
(44 + -1b) * b = 60

Reorder the terms for easier multiplication:
b(44 + -1b) = 60
(44 * b + -1b * b) = 60
(44b + -1b2) = 60

Solving
44b + -1b2 = 60

Solving for variable 'b'.

Reorder the terms:
-60 + 44b + -1b2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 44b + -1b2 = 0

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

Divide each side by '-1'.
60 + -44b + b2 = 0

Move the constant term to the right:

Add '-60' to each side of the equation.
60 + -44b + -60 + b2 = 0 + -60

Reorder the terms:
60 + -60 + -44b + b2 = 0 + -60

Combine like terms: 60 + -60 = 0
0 + -44b + b2 = 0 + -60
-44b + b2 = 0 + -60

Combine like terms: 0 + -60 = -60
-44b + b2 = -60

The b term is -44b.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44b + 484 + b2 = -60 + 484

Reorder the terms:
484 + -44b + b2 = -60 + 484

Combine like terms: -60 + 484 = 424
484 + -44b + b2 = 424

Factor a perfect square on the left side:
(b + -22)(b + -22) = 424

Calculate the square root of the right side: 20.591260282

Break this problem into two subproblems by setting 
(b + -22) equal to 20.591260282 and -20.591260282.

Subproblem 1

b + -22 = 20.591260282 Simplifying b + -22 = 20.591260282 Reorder the terms: -22 + b = 20.591260282 Solving -22 + b = 20.591260282 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + b = 20.591260282 + 22 Combine like terms: -22 + 22 = 0 0 + b = 20.591260282 + 22 b = 20.591260282 + 22 Combine like terms: 20.591260282 + 22 = 42.591260282 b = 42.591260282 Simplifying b = 42.591260282

Subproblem 2

b + -22 = -20.591260282 Simplifying b + -22 = -20.591260282 Reorder the terms: -22 + b = -20.591260282 Solving -22 + b = -20.591260282 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + b = -20.591260282 + 22 Combine like terms: -22 + 22 = 0 0 + b = -20.591260282 + 22 b = -20.591260282 + 22 Combine like terms: -20.591260282 + 22 = 1.408739718 b = 1.408739718 Simplifying b = 1.408739718

Solution

The solution to the problem is based on the solutions from the subproblems. b = {42.591260282, 1.408739718}

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