6v^2=-2v-1

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Solution for 6v^2=-2v-1 equation:


Simplifying
6v2 = -2v + -1

Reorder the terms:
6v2 = -1 + -2v

Solving
6v2 = -1 + -2v

Solving for variable 'v'.

Reorder the terms:
1 + 2v + 6v2 = -1 + -2v + 1 + 2v

Reorder the terms:
1 + 2v + 6v2 = -1 + 1 + -2v + 2v

Combine like terms: -1 + 1 = 0
1 + 2v + 6v2 = 0 + -2v + 2v
1 + 2v + 6v2 = -2v + 2v

Combine like terms: -2v + 2v = 0
1 + 2v + 6v2 = 0

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

Divide each side by '6'.
0.1666666667 + 0.3333333333v + v2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 0.3333333333v + -0.1666666667 + v2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 0.3333333333v + v2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 0.3333333333v + v2 = 0 + -0.1666666667
0.3333333333v + v2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
0.3333333333v + v2 = -0.1666666667

The v term is 0.3333333333v.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333v + 0.02777777779 + v2 = -0.1666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333v + v2 = -0.1666666667 + 0.02777777779

Combine like terms: -0.1666666667 + 0.02777777779 = -0.13888888891
0.02777777779 + 0.3333333333v + v2 = -0.13888888891

Factor a perfect square on the left side:
(v + 0.1666666667)(v + 0.1666666667) = -0.13888888891

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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