2(v+6)(v+6)=96

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Solution for 2(v+6)(v+6)=96 equation: 


Simplifying
2(v + 6)(v + 6) = 96

Reorder the terms:
2(6 + v)(v + 6) = 96

Reorder the terms:
2(6 + v)(6 + v) = 96

Multiply (6 + v) * (6 + v)
2(6(6 + v) + v(6 + v)) = 96
2((6 * 6 + v * 6) + v(6 + v)) = 96
2((36 + 6v) + v(6 + v)) = 96
2(36 + 6v + (6 * v + v * v)) = 96
2(36 + 6v + (6v + v2)) = 96

Combine like terms: 6v + 6v = 12v
2(36 + 12v + v2) = 96
(36 * 2 + 12v * 2 + v2 * 2) = 96
(72 + 24v + 2v2) = 96

Solving
72 + 24v + 2v2 = 96

Solving for variable 'v'.

Reorder the terms:
72 + -96 + 24v + 2v2 = 96 + -96

Combine like terms: 72 + -96 = -24
-24 + 24v + 2v2 = 96 + -96

Combine like terms: 96 + -96 = 0
-24 + 24v + 2v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 12v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-12 + 12v + v2)' equal to zero and attempt to solve:

Simplifying
-12 + 12v + v2 = 0

Solving
-12 + 12v + v2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The v term is 12v.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12v + 36 + v2 = 12 + 36

Reorder the terms:
36 + 12v + v2 = 12 + 36

Combine like terms: 12 + 36 = 48
36 + 12v + v2 = 48

Factor a perfect square on the left side:
(v + 6)(v + 6) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(v + 6) equal to 6.92820323 and -6.92820323.


Subproblem 1
v + 6 = 6.92820323

Simplifying
v + 6 = 6.92820323

Reorder the terms:
6 + v = 6.92820323

Solving
6 + v = 6.92820323

Solving for variable 'v'.

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

Add '-6' to each side of the equation.
6 + -6 + v = 6.92820323 + -6

Combine like terms: 6 + -6 = 0
0 + v = 6.92820323 + -6
v = 6.92820323 + -6

Combine like terms: 6.92820323 + -6 = 0.92820323
v = 0.92820323

Simplifying
v = 0.92820323


Subproblem 2
v + 6 = -6.92820323

Simplifying
v + 6 = -6.92820323

Reorder the terms:
6 + v = -6.92820323

Solving
6 + v = -6.92820323

Solving for variable 'v'.

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

Add '-6' to each side of the equation.
6 + -6 + v = -6.92820323 + -6

Combine like terms: 6 + -6 = 0
0 + v = -6.92820323 + -6
v = -6.92820323 + -6

Combine like terms: -6.92820323 + -6 = -12.92820323
v = -12.92820323

Simplifying
v = -12.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.92820323, -12.92820323}
Solution
v = {0.92820323, -12.92820323}

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