12b^2-b-190=0

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Solution for 12b^2-b-190=0 equation: 


Simplifying
12b2 + -1b + -190 = 0

Reorder the terms:
-190 + -1b + 12b2 = 0

Solving
-190 + -1b + 12b2 = 0

Solving for variable 'b'.

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

Divide each side by '12'.
-15.83333333 + -0.08333333333b + b2 = 0

Move the constant term to the right:

Add '15.83333333' to each side of the equation.
-15.83333333 + -0.08333333333b + 15.83333333 + b2 = 0 + 15.83333333

Reorder the terms:
-15.83333333 + 15.83333333 + -0.08333333333b + b2 = 0 + 15.83333333

Combine like terms: -15.83333333 + 15.83333333 = 0.00000000
0.00000000 + -0.08333333333b + b2 = 0 + 15.83333333
-0.08333333333b + b2 = 0 + 15.83333333

Combine like terms: 0 + 15.83333333 = 15.83333333
-0.08333333333b + b2 = 15.83333333

The b term is -0.08333333333b.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333b + 0.001736111111 + b2 = 15.83333333 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333b + b2 = 15.83333333 + 0.001736111111

Combine like terms: 15.83333333 + 0.001736111111 = 15.835069441111
0.001736111111 + -0.08333333333b + b2 = 15.835069441111

Factor a perfect square on the left side:
(b + -0.04166666667)(b + -0.04166666667) = 15.835069441111

Calculate the square root of the right side: 3.979330275

Break this problem into two subproblems by setting 
(b + -0.04166666667) equal to 3.979330275 and -3.979330275.


Subproblem 1
b + -0.04166666667 = 3.979330275

Simplifying
b + -0.04166666667 = 3.979330275

Reorder the terms:
-0.04166666667 + b = 3.979330275

Solving
-0.04166666667 + b = 3.979330275

Solving for variable 'b'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + b = 3.979330275 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + b = 3.979330275 + 0.04166666667
b = 3.979330275 + 0.04166666667

Combine like terms: 3.979330275 + 0.04166666667 = 4.02099694167
b = 4.02099694167

Simplifying
b = 4.02099694167


Subproblem 2
b + -0.04166666667 = -3.979330275

Simplifying
b + -0.04166666667 = -3.979330275

Reorder the terms:
-0.04166666667 + b = -3.979330275

Solving
-0.04166666667 + b = -3.979330275

Solving for variable 'b'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + b = -3.979330275 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + b = -3.979330275 + 0.04166666667
b = -3.979330275 + 0.04166666667

Combine like terms: -3.979330275 + 0.04166666667 = -3.93766360833
b = -3.93766360833

Simplifying
b = -3.93766360833


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.02099694167, -3.93766360833}

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