v^2+16v-12=-7

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Solution for v^2+16v-12=-7 equation: 


Simplifying
v2 + 16v + -12 = -7

Reorder the terms:
-12 + 16v + v2 = -7

Solving
-12 + 16v + v2 = -7

Solving for variable 'v'.

Reorder the terms:
-12 + 7 + 16v + v2 = -7 + 7

Combine like terms: -12 + 7 = -5
-5 + 16v + v2 = -7 + 7

Combine like terms: -7 + 7 = 0
-5 + 16v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 16v + 5 + v2 = 0 + 5

Reorder the terms:
-5 + 5 + 16v + v2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 16v + v2 = 0 + 5
16v + v2 = 0 + 5

Combine like terms: 0 + 5 = 5
16v + v2 = 5

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 = 5 + 64

Reorder the terms:
64 + 16v + v2 = 5 + 64

Combine like terms: 5 + 64 = 69
64 + 16v + v2 = 69

Factor a perfect square on the left side:
(v + 8)(v + 8) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(v + 8) equal to 8.306623863 and -8.306623863.


Subproblem 1
v + 8 = 8.306623863

Simplifying
v + 8 = 8.306623863

Reorder the terms:
8 + v = 8.306623863

Solving
8 + v = 8.306623863

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 = 8.306623863 + -8

Combine like terms: 8 + -8 = 0
0 + v = 8.306623863 + -8
v = 8.306623863 + -8

Combine like terms: 8.306623863 + -8 = 0.306623863
v = 0.306623863

Simplifying
v = 0.306623863


Subproblem 2
v + 8 = -8.306623863

Simplifying
v + 8 = -8.306623863

Reorder the terms:
8 + v = -8.306623863

Solving
8 + v = -8.306623863

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 = -8.306623863 + -8

Combine like terms: 8 + -8 = 0
0 + v = -8.306623863 + -8
v = -8.306623863 + -8

Combine like terms: -8.306623863 + -8 = -16.306623863
v = -16.306623863

Simplifying
v = -16.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.306623863, -16.306623863}

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