v^2+16v+64=13

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Solution for v^2+16v+64=13 equation: 


Simplifying
v2 + 16v + 64 = 13

Reorder the terms:
64 + 16v + v2 = 13

Solving
64 + 16v + v2 = 13

Solving for variable 'v'.

Reorder the terms:
64 + -13 + 16v + v2 = 13 + -13

Combine like terms: 64 + -13 = 51
51 + 16v + v2 = 13 + -13

Combine like terms: 13 + -13 = 0
51 + 16v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + 16v + -51 + v2 = 0 + -51

Reorder the terms:
51 + -51 + 16v + v2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 16v + v2 = 0 + -51
16v + v2 = 0 + -51

Combine like terms: 0 + -51 = -51
16v + v2 = -51

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 = -51 + 64

Reorder the terms:
64 + 16v + v2 = -51 + 64

Combine like terms: -51 + 64 = 13
64 + 16v + v2 = 13

Factor a perfect square on the left side:
(v + 8)(v + 8) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(v + 8) equal to 3.605551275 and -3.605551275.


Subproblem 1
v + 8 = 3.605551275

Simplifying
v + 8 = 3.605551275

Reorder the terms:
8 + v = 3.605551275

Solving
8 + v = 3.605551275

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 = 3.605551275 + -8

Combine like terms: 8 + -8 = 0
0 + v = 3.605551275 + -8
v = 3.605551275 + -8

Combine like terms: 3.605551275 + -8 = -4.394448725
v = -4.394448725

Simplifying
v = -4.394448725


Subproblem 2
v + 8 = -3.605551275

Simplifying
v + 8 = -3.605551275

Reorder the terms:
8 + v = -3.605551275

Solving
8 + v = -3.605551275

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 = -3.605551275 + -8

Combine like terms: 8 + -8 = 0
0 + v = -3.605551275 + -8
v = -3.605551275 + -8

Combine like terms: -3.605551275 + -8 = -11.605551275
v = -11.605551275

Simplifying
v = -11.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-4.394448725, -11.605551275}

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