2v^2+8v-16=0

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Solution for 2v^2+8v-16=0 equation: 


Simplifying
2v2 + 8v + -16 = 0

Reorder the terms:
-16 + 8v + 2v2 = 0

Solving
-16 + 8v + 2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 4v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + 4v + v2)' equal to zero and attempt to solve:

Simplifying
-8 + 4v + v2 = 0

Solving
-8 + 4v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 4v + 8 + v2 = 0 + 8

Reorder the terms:
-8 + 8 + 4v + v2 = 0 + 8

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

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

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 = 8 + 4

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

Combine like terms: 8 + 4 = 12
4 + 4v + v2 = 12

Factor a perfect square on the left side:
(v + 2)(v + 2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(v + 2) equal to 3.464101615 and -3.464101615.


Subproblem 1
v + 2 = 3.464101615

Simplifying
v + 2 = 3.464101615

Reorder the terms:
2 + v = 3.464101615

Solving
2 + v = 3.464101615

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 = 3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + v = 3.464101615 + -2
v = 3.464101615 + -2

Combine like terms: 3.464101615 + -2 = 1.464101615
v = 1.464101615

Simplifying
v = 1.464101615


Subproblem 2
v + 2 = -3.464101615

Simplifying
v + 2 = -3.464101615

Reorder the terms:
2 + v = -3.464101615

Solving
2 + v = -3.464101615

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 = -3.464101615 + -2

Combine like terms: 2 + -2 = 0
0 + v = -3.464101615 + -2
v = -3.464101615 + -2

Combine like terms: -3.464101615 + -2 = -5.464101615
v = -5.464101615

Simplifying
v = -5.464101615


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.464101615, -5.464101615}
Solution
v = {1.464101615, -5.464101615}

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