V(8+6V-6)=310

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Solution for V(8+6V-6)=310 equation: 


Simplifying
V(8 + 6V + -6) = 310

Reorder the terms:
V(8 + -6 + 6V) = 310

Combine like terms: 8 + -6 = 2
V(2 + 6V) = 310
(2 * V + 6V * V) = 310
(2V + 6V2) = 310

Solving
2V + 6V2 = 310

Solving for variable 'V'.

Reorder the terms:
-310 + 2V + 6V2 = 310 + -310

Combine like terms: 310 + -310 = 0
-310 + 2V + 6V2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-155 + V + 3V2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-155 + V + 3V2)' equal to zero and attempt to solve:

Simplifying
-155 + V + 3V2 = 0

Solving
-155 + V + 3V2 = 0

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

Divide each side by '3'.
-51.66666667 + 0.3333333333V + V2 = 0

Move the constant term to the right:

Add '51.66666667' to each side of the equation.
-51.66666667 + 0.3333333333V + 51.66666667 + V2 = 0 + 51.66666667

Reorder the terms:
-51.66666667 + 51.66666667 + 0.3333333333V + V2 = 0 + 51.66666667

Combine like terms: -51.66666667 + 51.66666667 = 0.00000000
0.00000000 + 0.3333333333V + V2 = 0 + 51.66666667
0.3333333333V + V2 = 0 + 51.66666667

Combine like terms: 0 + 51.66666667 = 51.66666667
0.3333333333V + V2 = 51.66666667

The V term is V.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333V + 0.25 + V2 = 51.66666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333V + V2 = 51.66666667 + 0.25

Combine like terms: 51.66666667 + 0.25 = 51.91666667
0.25 + 0.3333333333V + V2 = 51.91666667

Factor a perfect square on the left side:
(V + 0.5)(V + 0.5) = 51.91666667

Calculate the square root of the right side: 7.205322107

Break this problem into two subproblems by setting 
(V + 0.5) equal to 7.205322107 and -7.205322107.


Subproblem 1
V + 0.5 = 7.205322107

Simplifying
V + 0.5 = 7.205322107

Reorder the terms:
0.5 + V = 7.205322107

Solving
0.5 + V = 7.205322107

Solving for variable 'V'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + V = 7.205322107 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + V = 7.205322107 + -0.5
V = 7.205322107 + -0.5

Combine like terms: 7.205322107 + -0.5 = 6.705322107
V = 6.705322107

Simplifying
V = 6.705322107


Subproblem 2
V + 0.5 = -7.205322107

Simplifying
V + 0.5 = -7.205322107

Reorder the terms:
0.5 + V = -7.205322107

Solving
0.5 + V = -7.205322107

Solving for variable 'V'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + V = -7.205322107 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + V = -7.205322107 + -0.5
V = -7.205322107 + -0.5

Combine like terms: -7.205322107 + -0.5 = -7.705322107
V = -7.705322107

Simplifying
V = -7.705322107


Solution
The solution to the problem is based on the solutions
from the subproblems.
V = {6.705322107, -7.705322107}
Solution
V = {6.705322107, -7.705322107}

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