6v^2+11v+1=0

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Solution for 6v^2+11v+1=0 equation: 


Simplifying
6v2 + 11v + 1 = 0

Reorder the terms:
1 + 11v + 6v2 = 0

Solving
1 + 11v + 6v2 = 0

Solving for variable 'v'.

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

Divide each side by '6'.
0.1666666667 + 1.833333333v + v2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 1.833333333v + -0.1666666667 + v2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 1.833333333v + v2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 1.833333333v + v2 = 0 + -0.1666666667
1.833333333v + v2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
1.833333333v + v2 = -0.1666666667

The v term is 1.833333333v.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333v + 0.8402777775 + v2 = -0.1666666667 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333v + v2 = -0.1666666667 + 0.8402777775

Combine like terms: -0.1666666667 + 0.8402777775 = 0.6736111108
0.8402777775 + 1.833333333v + v2 = 0.6736111108

Factor a perfect square on the left side:
(v + 0.9166666665)(v + 0.9166666665) = 0.6736111108

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(v + 0.9166666665) equal to 0.82073815 and -0.82073815.


Subproblem 1
v + 0.9166666665 = 0.82073815

Simplifying
v + 0.9166666665 = 0.82073815

Reorder the terms:
0.9166666665 + v = 0.82073815

Solving
0.9166666665 + v = 0.82073815

Solving for variable 'v'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + v = 0.82073815 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + v = 0.82073815 + -0.9166666665
v = 0.82073815 + -0.9166666665

Combine like terms: 0.82073815 + -0.9166666665 = -0.0959285165
v = -0.0959285165

Simplifying
v = -0.0959285165


Subproblem 2
v + 0.9166666665 = -0.82073815

Simplifying
v + 0.9166666665 = -0.82073815

Reorder the terms:
0.9166666665 + v = -0.82073815

Solving
0.9166666665 + v = -0.82073815

Solving for variable 'v'.

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

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + v = -0.82073815 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + v = -0.82073815 + -0.9166666665
v = -0.82073815 + -0.9166666665

Combine like terms: -0.82073815 + -0.9166666665 = -1.7374048165
v = -1.7374048165

Simplifying
v = -1.7374048165


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.0959285165, -1.7374048165}

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