2v^2-8v-8=0

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Solution for 2v^2-8v-8=0 equation: 


Simplifying
2v2 + -8v + -8 = 0

Reorder the terms:
-8 + -8v + 2v2 = 0

Solving
-8 + -8v + 2v2 = 0

Solving for variable 'v'.

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -4v + v2)' equal to zero and attempt to solve:

Simplifying
-4 + -4v + v2 = 0

Solving
-4 + -4v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4v + 4 + v2 = 0 + 4

Reorder the terms:
-4 + 4 + -4v + v2 = 0 + 4

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

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

The v term is -4v.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4v + 4 + v2 = 4 + 4

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

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

Factor a perfect square on the left side:
(v + -2)(v + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(v + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
v + -2 = 2.828427125

Simplifying
v + -2 = 2.828427125

Reorder the terms:
-2 + v = 2.828427125

Solving
-2 + v = 2.828427125

Solving for variable 'v'.

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

Add '2' to each side of the equation.
-2 + 2 + v = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + v = 2.828427125 + 2
v = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
v = 4.828427125

Simplifying
v = 4.828427125


Subproblem 2
v + -2 = -2.828427125

Simplifying
v + -2 = -2.828427125

Reorder the terms:
-2 + v = -2.828427125

Solving
-2 + v = -2.828427125

Solving for variable 'v'.

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

Add '2' to each side of the equation.
-2 + 2 + v = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + v = -2.828427125 + 2
v = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
v = -0.828427125

Simplifying
v = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.828427125, -0.828427125}
Solution
v = {4.828427125, -0.828427125}

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