8v-4v(v+8)=8

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Solution for 8v-4v(v+8)=8 equation: 


Simplifying
8v + -4v(v + 8) = 8

Reorder the terms:
8v + -4v(8 + v) = 8
8v + (8 * -4v + v * -4v) = 8
8v + (-32v + -4v2) = 8

Combine like terms: 8v + -32v = -24v
-24v + -4v2 = 8

Solving
-24v + -4v2 = 8

Solving for variable 'v'.

Reorder the terms:
-8 + -24v + -4v2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -24v + -4v2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(2 + 6v + v2) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(2 + 6v + v2)' equal to zero and attempt to solve:

Simplifying
2 + 6v + v2 = 0

Solving
2 + 6v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6v + -2 + v2 = 0 + -2

Reorder the terms:
2 + -2 + 6v + v2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6v + v2 = 0 + -2
6v + v2 = 0 + -2

Combine like terms: 0 + -2 = -2
6v + v2 = -2

The v term is 6v.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6v + 9 + v2 = -2 + 9

Reorder the terms:
9 + 6v + v2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6v + v2 = 7

Factor a perfect square on the left side:
(v + 3)(v + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(v + 3) equal to 2.645751311 and -2.645751311.


Subproblem 1
v + 3 = 2.645751311

Simplifying
v + 3 = 2.645751311

Reorder the terms:
3 + v = 2.645751311

Solving
3 + v = 2.645751311

Solving for variable 'v'.

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

Add '-3' to each side of the equation.
3 + -3 + v = 2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + v = 2.645751311 + -3
v = 2.645751311 + -3

Combine like terms: 2.645751311 + -3 = -0.354248689
v = -0.354248689

Simplifying
v = -0.354248689


Subproblem 2
v + 3 = -2.645751311

Simplifying
v + 3 = -2.645751311

Reorder the terms:
3 + v = -2.645751311

Solving
3 + v = -2.645751311

Solving for variable 'v'.

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

Add '-3' to each side of the equation.
3 + -3 + v = -2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + v = -2.645751311 + -3
v = -2.645751311 + -3

Combine like terms: -2.645751311 + -3 = -5.645751311
v = -5.645751311

Simplifying
v = -5.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-0.354248689, -5.645751311}
Solution
v = {-0.354248689, -5.645751311}

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