12v^2-v-14=0

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Solution for 12v^2-v-14=0 equation: 


Simplifying
12v2 + -1v + -14 = 0

Reorder the terms:
-14 + -1v + 12v2 = 0

Solving
-14 + -1v + 12v2 = 0

Solving for variable 'v'.

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

Divide each side by '12'.
-1.166666667 + -0.08333333333v + v2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + -0.08333333333v + 1.166666667 + v2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + -0.08333333333v + v2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + -0.08333333333v + v2 = 0 + 1.166666667
-0.08333333333v + v2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
-0.08333333333v + v2 = 1.166666667

The v term is -0.08333333333v.  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.
-0.08333333333v + 0.001736111111 + v2 = 1.166666667 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333v + v2 = 1.166666667 + 0.001736111111

Combine like terms: 1.166666667 + 0.001736111111 = 1.168402778111
0.001736111111 + -0.08333333333v + v2 = 1.168402778111

Factor a perfect square on the left side:
(v + -0.04166666667)(v + -0.04166666667) = 1.168402778111

Calculate the square root of the right side: 1.080926814

Break this problem into two subproblems by setting 
(v + -0.04166666667) equal to 1.080926814 and -1.080926814.


Subproblem 1
v + -0.04166666667 = 1.080926814

Simplifying
v + -0.04166666667 = 1.080926814

Reorder the terms:
-0.04166666667 + v = 1.080926814

Solving
-0.04166666667 + v = 1.080926814

Solving for variable 'v'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + v = 1.080926814 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + v = 1.080926814 + 0.04166666667
v = 1.080926814 + 0.04166666667

Combine like terms: 1.080926814 + 0.04166666667 = 1.12259348067
v = 1.12259348067

Simplifying
v = 1.12259348067


Subproblem 2
v + -0.04166666667 = -1.080926814

Simplifying
v + -0.04166666667 = -1.080926814

Reorder the terms:
-0.04166666667 + v = -1.080926814

Solving
-0.04166666667 + v = -1.080926814

Solving for variable 'v'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + v = -1.080926814 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + v = -1.080926814 + 0.04166666667
v = -1.080926814 + 0.04166666667

Combine like terms: -1.080926814 + 0.04166666667 = -1.03926014733
v = -1.03926014733

Simplifying
v = -1.03926014733


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.12259348067, -1.03926014733}

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