3b^2-4b-101761=0

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Solution for 3b^2-4b-101761=0 equation: 


Simplifying
3b2 + -4b + -101761 = 0

Reorder the terms:
-101761 + -4b + 3b2 = 0

Solving
-101761 + -4b + 3b2 = 0

Solving for variable 'b'.

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

Divide each side by '3'.
-33920.33333 + -1.333333333b + b2 = 0

Move the constant term to the right:

Add '33920.33333' to each side of the equation.
-33920.33333 + -1.333333333b + 33920.33333 + b2 = 0 + 33920.33333

Reorder the terms:
-33920.33333 + 33920.33333 + -1.333333333b + b2 = 0 + 33920.33333

Combine like terms: -33920.33333 + 33920.33333 = 0.00000
0.00000 + -1.333333333b + b2 = 0 + 33920.33333
-1.333333333b + b2 = 0 + 33920.33333

Combine like terms: 0 + 33920.33333 = 33920.33333
-1.333333333b + b2 = 33920.33333

The b term is -1.333333333b.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333b + 0.4444444442 + b2 = 33920.33333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333b + b2 = 33920.33333 + 0.4444444442

Combine like terms: 33920.33333 + 0.4444444442 = 33920.7777744442
0.4444444442 + -1.333333333b + b2 = 33920.7777744442

Factor a perfect square on the left side:
(b + -0.6666666665)(b + -0.6666666665) = 33920.7777744442

Calculate the square root of the right side: 184.175942442

Break this problem into two subproblems by setting 
(b + -0.6666666665) equal to 184.175942442 and -184.175942442.


Subproblem 1
b + -0.6666666665 = 184.175942442

Simplifying
b + -0.6666666665 = 184.175942442

Reorder the terms:
-0.6666666665 + b = 184.175942442

Solving
-0.6666666665 + b = 184.175942442

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + b = 184.175942442 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + b = 184.175942442 + 0.6666666665
b = 184.175942442 + 0.6666666665

Combine like terms: 184.175942442 + 0.6666666665 = 184.8426091085
b = 184.8426091085

Simplifying
b = 184.8426091085


Subproblem 2
b + -0.6666666665 = -184.175942442

Simplifying
b + -0.6666666665 = -184.175942442

Reorder the terms:
-0.6666666665 + b = -184.175942442

Solving
-0.6666666665 + b = -184.175942442

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + b = -184.175942442 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + b = -184.175942442 + 0.6666666665
b = -184.175942442 + 0.6666666665

Combine like terms: -184.175942442 + 0.6666666665 = -183.5092757755
b = -183.5092757755

Simplifying
b = -183.5092757755


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {184.8426091085, -183.5092757755}

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