2v^2-18v-16=0

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Solution for 2v^2-18v-16=0 equation: 


Simplifying
2v2 + -18v + -16 = 0

Reorder the terms:
-16 + -18v + 2v2 = 0

Solving
-16 + -18v + 2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -9v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -9v + v2)' equal to zero and attempt to solve:

Simplifying
-8 + -9v + v2 = 0

Solving
-8 + -9v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -9v + 8 + v2 = 0 + 8

Reorder the terms:
-8 + 8 + -9v + v2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9v + v2 = 0 + 8
-9v + v2 = 0 + 8

Combine like terms: 0 + 8 = 8
-9v + v2 = 8

The v term is -9v.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9v + 20.25 + v2 = 8 + 20.25

Reorder the terms:
20.25 + -9v + v2 = 8 + 20.25

Combine like terms: 8 + 20.25 = 28.25
20.25 + -9v + v2 = 28.25

Factor a perfect square on the left side:
(v + -4.5)(v + -4.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(v + -4.5) equal to 5.315072906 and -5.315072906.


Subproblem 1
v + -4.5 = 5.315072906

Simplifying
v + -4.5 = 5.315072906

Reorder the terms:
-4.5 + v = 5.315072906

Solving
-4.5 + v = 5.315072906

Solving for variable 'v'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + v = 5.315072906 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + v = 5.315072906 + 4.5
v = 5.315072906 + 4.5

Combine like terms: 5.315072906 + 4.5 = 9.815072906
v = 9.815072906

Simplifying
v = 9.815072906


Subproblem 2
v + -4.5 = -5.315072906

Simplifying
v + -4.5 = -5.315072906

Reorder the terms:
-4.5 + v = -5.315072906

Solving
-4.5 + v = -5.315072906

Solving for variable 'v'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + v = -5.315072906 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + v = -5.315072906 + 4.5
v = -5.315072906 + 4.5

Combine like terms: -5.315072906 + 4.5 = -0.815072906
v = -0.815072906

Simplifying
v = -0.815072906


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {9.815072906, -0.815072906}
Solution
v = {9.815072906, -0.815072906}

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