2v^2+28v-34=0

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Solution for 2v^2+28v-34=0 equation: 


Simplifying
2v2 + 28v + -34 = 0

Reorder the terms:
-34 + 28v + 2v2 = 0

Solving
-34 + 28v + 2v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 14v + v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + 14v + v2)' equal to zero and attempt to solve:

Simplifying
-17 + 14v + v2 = 0

Solving
-17 + 14v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 14v + 17 + v2 = 0 + 17

Reorder the terms:
-17 + 17 + 14v + v2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 14v + v2 = 0 + 17
14v + v2 = 0 + 17

Combine like terms: 0 + 17 = 17
14v + v2 = 17

The v term is 14v.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14v + 49 + v2 = 17 + 49

Reorder the terms:
49 + 14v + v2 = 17 + 49

Combine like terms: 17 + 49 = 66
49 + 14v + v2 = 66

Factor a perfect square on the left side:
(v + 7)(v + 7) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(v + 7) equal to 8.124038405 and -8.124038405.


Subproblem 1
v + 7 = 8.124038405

Simplifying
v + 7 = 8.124038405

Reorder the terms:
7 + v = 8.124038405

Solving
7 + v = 8.124038405

Solving for variable 'v'.

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

Add '-7' to each side of the equation.
7 + -7 + v = 8.124038405 + -7

Combine like terms: 7 + -7 = 0
0 + v = 8.124038405 + -7
v = 8.124038405 + -7

Combine like terms: 8.124038405 + -7 = 1.124038405
v = 1.124038405

Simplifying
v = 1.124038405


Subproblem 2
v + 7 = -8.124038405

Simplifying
v + 7 = -8.124038405

Reorder the terms:
7 + v = -8.124038405

Solving
7 + v = -8.124038405

Solving for variable 'v'.

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

Add '-7' to each side of the equation.
7 + -7 + v = -8.124038405 + -7

Combine like terms: 7 + -7 = 0
0 + v = -8.124038405 + -7
v = -8.124038405 + -7

Combine like terms: -8.124038405 + -7 = -15.124038405
v = -15.124038405

Simplifying
v = -15.124038405


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.124038405, -15.124038405}
Solution
v = {1.124038405, -15.124038405}

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