v^2-16v-12=0

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Solution for v^2-16v-12=0 equation: 


Simplifying
v2 + -16v + -12 = 0

Reorder the terms:
-12 + -16v + v2 = 0

Solving
-12 + -16v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -16v + 12 + v2 = 0 + 12

Reorder the terms:
-12 + 12 + -16v + v2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -16v + v2 = 0 + 12
-16v + v2 = 0 + 12

Combine like terms: 0 + 12 = 12
-16v + v2 = 12

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 = 12 + 64

Reorder the terms:
64 + -16v + v2 = 12 + 64

Combine like terms: 12 + 64 = 76
64 + -16v + v2 = 76

Factor a perfect square on the left side:
(v + -8)(v + -8) = 76

Calculate the square root of the right side: 8.717797887

Break this problem into two subproblems by setting 
(v + -8) equal to 8.717797887 and -8.717797887.


Subproblem 1
v + -8 = 8.717797887

Simplifying
v + -8 = 8.717797887

Reorder the terms:
-8 + v = 8.717797887

Solving
-8 + v = 8.717797887

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 = 8.717797887 + 8

Combine like terms: -8 + 8 = 0
0 + v = 8.717797887 + 8
v = 8.717797887 + 8

Combine like terms: 8.717797887 + 8 = 16.717797887
v = 16.717797887

Simplifying
v = 16.717797887


Subproblem 2
v + -8 = -8.717797887

Simplifying
v + -8 = -8.717797887

Reorder the terms:
-8 + v = -8.717797887

Solving
-8 + v = -8.717797887

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 = -8.717797887 + 8

Combine like terms: -8 + 8 = 0
0 + v = -8.717797887 + 8
v = -8.717797887 + 8

Combine like terms: -8.717797887 + 8 = -0.717797887
v = -0.717797887

Simplifying
v = -0.717797887


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {16.717797887, -0.717797887}

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