b^2-77b+12=0

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Solution for b^2-77b+12=0 equation:


Simplifying
b2 + -77b + 12 = 0

Reorder the terms:
12 + -77b + b2 = 0

Solving
12 + -77b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -77b + -12 + b2 = 0 + -12

Reorder the terms:
12 + -12 + -77b + b2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -77b + b2 = 0 + -12
-77b + b2 = 0 + -12

Combine like terms: 0 + -12 = -12
-77b + b2 = -12

The b term is -77b.  Take half its coefficient (-38.5).
Square it (1482.25) and add it to both sides.

Add '1482.25' to each side of the equation.
-77b + 1482.25 + b2 = -12 + 1482.25

Reorder the terms:
1482.25 + -77b + b2 = -12 + 1482.25

Combine like terms: -12 + 1482.25 = 1470.25
1482.25 + -77b + b2 = 1470.25

Factor a perfect square on the left side:
(b + -38.5)(b + -38.5) = 1470.25

Calculate the square root of the right side: 38.34383914

Break this problem into two subproblems by setting 
(b + -38.5) equal to 38.34383914 and -38.34383914.

Subproblem 1

b + -38.5 = 38.34383914 Simplifying b + -38.5 = 38.34383914 Reorder the terms: -38.5 + b = 38.34383914 Solving -38.5 + b = 38.34383914 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '38.5' to each side of the equation. -38.5 + 38.5 + b = 38.34383914 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + b = 38.34383914 + 38.5 b = 38.34383914 + 38.5 Combine like terms: 38.34383914 + 38.5 = 76.84383914 b = 76.84383914 Simplifying b = 76.84383914

Subproblem 2

b + -38.5 = -38.34383914 Simplifying b + -38.5 = -38.34383914 Reorder the terms: -38.5 + b = -38.34383914 Solving -38.5 + b = -38.34383914 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '38.5' to each side of the equation. -38.5 + 38.5 + b = -38.34383914 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + b = -38.34383914 + 38.5 b = -38.34383914 + 38.5 Combine like terms: -38.34383914 + 38.5 = 0.15616086 b = 0.15616086 Simplifying b = 0.15616086

Solution

The solution to the problem is based on the solutions from the subproblems. b = {76.84383914, 0.15616086}

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