1v^2+18v+5=0

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Solution for 1v^2+18v+5=0 equation: 


Simplifying
1v2 + 18v + 5 = 0

Reorder the terms:
5 + 18v + 1v2 = 0

Solving
5 + 18v + 1v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 18v + -5 + v2 = 0 + -5

Reorder the terms:
5 + -5 + 18v + v2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 18v + v2 = 0 + -5
18v + v2 = 0 + -5

Combine like terms: 0 + -5 = -5
18v + v2 = -5

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 = -5 + 81

Reorder the terms:
81 + 18v + v2 = -5 + 81

Combine like terms: -5 + 81 = 76
81 + 18v + v2 = 76

Factor a perfect square on the left side:
(v + 9)(v + 9) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(v + 9) equal to 8.717797887 and -8.717797887.


Subproblem 1
v + 9 = 8.717797887

Simplifying
v + 9 = 8.717797887

Reorder the terms:
9 + v = 8.717797887

Solving
9 + v = 8.717797887

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 = 8.717797887 + -9

Combine like terms: 9 + -9 = 0
0 + v = 8.717797887 + -9
v = 8.717797887 + -9

Combine like terms: 8.717797887 + -9 = -0.282202113
v = -0.282202113

Simplifying
v = -0.282202113


Subproblem 2
v + 9 = -8.717797887

Simplifying
v + 9 = -8.717797887

Reorder the terms:
9 + v = -8.717797887

Solving
9 + v = -8.717797887

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 = -8.717797887 + -9

Combine like terms: 9 + -9 = 0
0 + v = -8.717797887 + -9
v = -8.717797887 + -9

Combine like terms: -8.717797887 + -9 = -17.717797887
v = -17.717797887

Simplifying
v = -17.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.282202113, -17.717797887}

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