3v^2+6v-104=-7

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Solution for 3v^2+6v-104=-7 equation:


Simplifying
3v2 + 6v + -104 = -7

Reorder the terms:
-104 + 6v + 3v2 = -7

Solving
-104 + 6v + 3v2 = -7

Solving for variable 'v'.

Reorder the terms:
-104 + 7 + 6v + 3v2 = -7 + 7

Combine like terms: -104 + 7 = -97
-97 + 6v + 3v2 = -7 + 7

Combine like terms: -7 + 7 = 0
-97 + 6v + 3v2 = 0

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

Divide each side by '3'.
-32.33333333 + 2v + v2 = 0

Move the constant term to the right:

Add '32.33333333' to each side of the equation.
-32.33333333 + 2v + 32.33333333 + v2 = 0 + 32.33333333

Reorder the terms:
-32.33333333 + 32.33333333 + 2v + v2 = 0 + 32.33333333

Combine like terms: -32.33333333 + 32.33333333 = 0.00000000
0.00000000 + 2v + v2 = 0 + 32.33333333
2v + v2 = 0 + 32.33333333

Combine like terms: 0 + 32.33333333 = 32.33333333
2v + v2 = 32.33333333

The v term is 2v.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2v + 1 + v2 = 32.33333333 + 1

Reorder the terms:
1 + 2v + v2 = 32.33333333 + 1

Combine like terms: 32.33333333 + 1 = 33.33333333
1 + 2v + v2 = 33.33333333

Factor a perfect square on the left side:
(v + 1)(v + 1) = 33.33333333

Calculate the square root of the right side: 5.773502692

Break this problem into two subproblems by setting 
(v + 1) equal to 5.773502692 and -5.773502692.

Subproblem 1

v + 1 = 5.773502692 Simplifying v + 1 = 5.773502692 Reorder the terms: 1 + v = 5.773502692 Solving 1 + v = 5.773502692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 5.773502692 + -1 Combine like terms: 1 + -1 = 0 0 + v = 5.773502692 + -1 v = 5.773502692 + -1 Combine like terms: 5.773502692 + -1 = 4.773502692 v = 4.773502692 Simplifying v = 4.773502692

Subproblem 2

v + 1 = -5.773502692 Simplifying v + 1 = -5.773502692 Reorder the terms: 1 + v = -5.773502692 Solving 1 + v = -5.773502692 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = -5.773502692 + -1 Combine like terms: 1 + -1 = 0 0 + v = -5.773502692 + -1 v = -5.773502692 + -1 Combine like terms: -5.773502692 + -1 = -6.773502692 v = -6.773502692 Simplifying v = -6.773502692

Solution

The solution to the problem is based on the solutions from the subproblems. v = {4.773502692, -6.773502692}

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