v^2+7.3v-65.7=0

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Solution for v^2+7.3v-65.7=0 equation: 


Simplifying
v2 + 7.3v + -65.7 = 0

Reorder the terms:
-65.7 + 7.3v + v2 = 0

Solving
-65.7 + 7.3v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '65.7' to each side of the equation.
-65.7 + 7.3v + 65.7 + v2 = 0 + 65.7

Reorder the terms:
-65.7 + 65.7 + 7.3v + v2 = 0 + 65.7

Combine like terms: -65.7 + 65.7 = 0.0
0.0 + 7.3v + v2 = 0 + 65.7
7.3v + v2 = 0 + 65.7

Combine like terms: 0 + 65.7 = 65.7
7.3v + v2 = 65.7

The v term is 7.3v.  Take half its coefficient (3.65).
Square it (13.3225) and add it to both sides.

Add '13.3225' to each side of the equation.
7.3v + 13.3225 + v2 = 65.7 + 13.3225

Reorder the terms:
13.3225 + 7.3v + v2 = 65.7 + 13.3225

Combine like terms: 65.7 + 13.3225 = 79.0225
13.3225 + 7.3v + v2 = 79.0225

Factor a perfect square on the left side:
(v + 3.65)(v + 3.65) = 79.0225

Calculate the square root of the right side: 8.889460051

Break this problem into two subproblems by setting 
(v + 3.65) equal to 8.889460051 and -8.889460051.


Subproblem 1
v + 3.65 = 8.889460051

Simplifying
v + 3.65 = 8.889460051

Reorder the terms:
3.65 + v = 8.889460051

Solving
3.65 + v = 8.889460051

Solving for variable 'v'.

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

Add '-3.65' to each side of the equation.
3.65 + -3.65 + v = 8.889460051 + -3.65

Combine like terms: 3.65 + -3.65 = 0.00
0.00 + v = 8.889460051 + -3.65
v = 8.889460051 + -3.65

Combine like terms: 8.889460051 + -3.65 = 5.239460051
v = 5.239460051

Simplifying
v = 5.239460051


Subproblem 2
v + 3.65 = -8.889460051

Simplifying
v + 3.65 = -8.889460051

Reorder the terms:
3.65 + v = -8.889460051

Solving
3.65 + v = -8.889460051

Solving for variable 'v'.

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

Add '-3.65' to each side of the equation.
3.65 + -3.65 + v = -8.889460051 + -3.65

Combine like terms: 3.65 + -3.65 = 0.00
0.00 + v = -8.889460051 + -3.65
v = -8.889460051 + -3.65

Combine like terms: -8.889460051 + -3.65 = -12.539460051
v = -12.539460051

Simplifying
v = -12.539460051


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {5.239460051, -12.539460051}

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