v^2+16v-165=0

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Solution for v^2+16v-165=0 equation: 


Simplifying
v2 + 16v + -165 = 0

Reorder the terms:
-165 + 16v + v2 = 0

Solving
-165 + 16v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '165' to each side of the equation.
-165 + 16v + 165 + v2 = 0 + 165

Reorder the terms:
-165 + 165 + 16v + v2 = 0 + 165

Combine like terms: -165 + 165 = 0
0 + 16v + v2 = 0 + 165
16v + v2 = 0 + 165

Combine like terms: 0 + 165 = 165
16v + v2 = 165

The v term is 16v.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16v + 64 + v2 = 165 + 64

Reorder the terms:
64 + 16v + v2 = 165 + 64

Combine like terms: 165 + 64 = 229
64 + 16v + v2 = 229

Factor a perfect square on the left side:
(v + 8)(v + 8) = 229

Calculate the square root of the right side: 15.13274595

Break this problem into two subproblems by setting 
(v + 8) equal to 15.13274595 and -15.13274595.


Subproblem 1
v + 8 = 15.13274595

Simplifying
v + 8 = 15.13274595

Reorder the terms:
8 + v = 15.13274595

Solving
8 + v = 15.13274595

Solving for variable 'v'.

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

Add '-8' to each side of the equation.
8 + -8 + v = 15.13274595 + -8

Combine like terms: 8 + -8 = 0
0 + v = 15.13274595 + -8
v = 15.13274595 + -8

Combine like terms: 15.13274595 + -8 = 7.13274595
v = 7.13274595

Simplifying
v = 7.13274595


Subproblem 2
v + 8 = -15.13274595

Simplifying
v + 8 = -15.13274595

Reorder the terms:
8 + v = -15.13274595

Solving
8 + v = -15.13274595

Solving for variable 'v'.

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

Add '-8' to each side of the equation.
8 + -8 + v = -15.13274595 + -8

Combine like terms: 8 + -8 = 0
0 + v = -15.13274595 + -8
v = -15.13274595 + -8

Combine like terms: -15.13274595 + -8 = -23.13274595
v = -23.13274595

Simplifying
v = -23.13274595


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {7.13274595, -23.13274595}

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