b^2-2b-72=0

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Solution for b^2-2b-72=0 equation:


Simplifying
b2 + -2b + -72 = 0

Reorder the terms:
-72 + -2b + b2 = 0

Solving
-72 + -2b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -2b + 72 + b2 = 0 + 72

Reorder the terms:
-72 + 72 + -2b + b2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -2b + b2 = 0 + 72
-2b + b2 = 0 + 72

Combine like terms: 0 + 72 = 72
-2b + b2 = 72

The b term is -2b.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2b + 1 + b2 = 72 + 1

Reorder the terms:
1 + -2b + b2 = 72 + 1

Combine like terms: 72 + 1 = 73
1 + -2b + b2 = 73

Factor a perfect square on the left side:
(b + -1)(b + -1) = 73

Calculate the square root of the right side: 8.544003745

Break this problem into two subproblems by setting 
(b + -1) equal to 8.544003745 and -8.544003745.

Subproblem 1

b + -1 = 8.544003745 Simplifying b + -1 = 8.544003745 Reorder the terms: -1 + b = 8.544003745 Solving -1 + b = 8.544003745 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = 8.544003745 + 1 Combine like terms: -1 + 1 = 0 0 + b = 8.544003745 + 1 b = 8.544003745 + 1 Combine like terms: 8.544003745 + 1 = 9.544003745 b = 9.544003745 Simplifying b = 9.544003745

Subproblem 2

b + -1 = -8.544003745 Simplifying b + -1 = -8.544003745 Reorder the terms: -1 + b = -8.544003745 Solving -1 + b = -8.544003745 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + b = -8.544003745 + 1 Combine like terms: -1 + 1 = 0 0 + b = -8.544003745 + 1 b = -8.544003745 + 1 Combine like terms: -8.544003745 + 1 = -7.544003745 b = -7.544003745 Simplifying b = -7.544003745

Solution

The solution to the problem is based on the solutions from the subproblems. b = {9.544003745, -7.544003745}

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