V^2+18V+27=0

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Solution for V^2+18V+27=0 equation: 


Simplifying
V2 + 18V + 27 = 0

Reorder the terms:
27 + 18V + V2 = 0

Solving
27 + 18V + V2 = 0

Solving for variable 'V'.

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 18V + -27 + V2 = 0 + -27

Reorder the terms:
27 + -27 + 18V + V2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 18V + V2 = 0 + -27
18V + V2 = 0 + -27

Combine like terms: 0 + -27 = -27
18V + V2 = -27

The V term is 18V.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18V + 81 + V2 = -27 + 81

Reorder the terms:
81 + 18V + V2 = -27 + 81

Combine like terms: -27 + 81 = 54
81 + 18V + V2 = 54

Factor a perfect square on the left side:
(V + 9)(V + 9) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(V + 9) equal to 7.348469228 and -7.348469228.


Subproblem 1
V + 9 = 7.348469228

Simplifying
V + 9 = 7.348469228

Reorder the terms:
9 + V = 7.348469228

Solving
9 + V = 7.348469228

Solving for variable 'V'.

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

Add '-9' to each side of the equation.
9 + -9 + V = 7.348469228 + -9

Combine like terms: 9 + -9 = 0
0 + V = 7.348469228 + -9
V = 7.348469228 + -9

Combine like terms: 7.348469228 + -9 = -1.651530772
V = -1.651530772

Simplifying
V = -1.651530772


Subproblem 2
V + 9 = -7.348469228

Simplifying
V + 9 = -7.348469228

Reorder the terms:
9 + V = -7.348469228

Solving
9 + V = -7.348469228

Solving for variable 'V'.

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

Add '-9' to each side of the equation.
9 + -9 + V = -7.348469228 + -9

Combine like terms: 9 + -9 = 0
0 + V = -7.348469228 + -9
V = -7.348469228 + -9

Combine like terms: -7.348469228 + -9 = -16.348469228
V = -16.348469228

Simplifying
V = -16.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
V = {-1.651530772, -16.348469228}

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