8=8v(v+8)

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


Simplifying
8 = 8v(v + 8)

Reorder the terms:
8 = 8v(8 + v)
8 = (8 * 8v + v * 8v)
8 = (64v + 8v2)

Solving
8 = 64v + 8v2

Solving for variable 'v'.

Reorder the terms:
8 + -64v + -8v2 = 64v + -64v + 8v2 + -8v2

Combine like terms: 64v + -64v = 0
8 + -64v + -8v2 = 0 + 8v2 + -8v2
8 + -64v + -8v2 = 8v2 + -8v2

Combine like terms: 8v2 + -8v2 = 0
8 + -64v + -8v2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -8v + -1v2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(1 + -8v + -1v2)' equal to zero and attempt to solve:

Simplifying
1 + -8v + -1v2 = 0

Solving
1 + -8v + -1v2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + 8v + v2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 8v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + 8v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 8v + v2 = 0 + 1
8v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
8v + v2 = 1

The v term is 8v.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8v + 16 + v2 = 1 + 16

Reorder the terms:
16 + 8v + v2 = 1 + 16

Combine like terms: 1 + 16 = 17
16 + 8v + v2 = 17

Factor a perfect square on the left side:
(v + 4)(v + 4) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(v + 4) equal to 4.123105626 and -4.123105626.


Subproblem 1
v + 4 = 4.123105626

Simplifying
v + 4 = 4.123105626

Reorder the terms:
4 + v = 4.123105626

Solving
4 + v = 4.123105626

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = 4.123105626 + -4

Combine like terms: 4 + -4 = 0
0 + v = 4.123105626 + -4
v = 4.123105626 + -4

Combine like terms: 4.123105626 + -4 = 0.123105626
v = 0.123105626

Simplifying
v = 0.123105626


Subproblem 2
v + 4 = -4.123105626

Simplifying
v + 4 = -4.123105626

Reorder the terms:
4 + v = -4.123105626

Solving
4 + v = -4.123105626

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = -4.123105626 + -4

Combine like terms: 4 + -4 = 0
0 + v = -4.123105626 + -4
v = -4.123105626 + -4

Combine like terms: -4.123105626 + -4 = -8.123105626
v = -8.123105626

Simplifying
v = -8.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.123105626, -8.123105626}
Solution
v = {0.123105626, -8.123105626}

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