7v^2+14v-38=0

Solution for 7v^2+14v-38=0 equation:

Simplifying
7v2 + 14v + -38 = 0

Reorder the terms:
-38 + 14v + 7v2 = 0

Solving
-38 + 14v + 7v2 = 0

Solving for variable 'v'.

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

Divide each side by '7'.
-5.428571429 + 2v + v2 = 0

Move the constant term to the right:

Add '5.428571429' to each side of the equation.
-5.428571429 + 2v + 5.428571429 + v2 = 0 + 5.428571429

Reorder the terms:
-5.428571429 + 5.428571429 + 2v + v2 = 0 + 5.428571429

Combine like terms: -5.428571429 + 5.428571429 = 0.000000000
0.000000000 + 2v + v2 = 0 + 5.428571429
2v + v2 = 0 + 5.428571429

Combine like terms: 0 + 5.428571429 = 5.428571429
2v + v2 = 5.428571429

The v term is 2v.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2v + 1 + v2 = 5.428571429 + 1

Reorder the terms:
1 + 2v + v2 = 5.428571429 + 1

Combine like terms: 5.428571429 + 1 = 6.428571429
1 + 2v + v2 = 6.428571429

Factor a perfect square on the left side:
(v + 1)(v + 1) = 6.428571429

Calculate the square root of the right side: 2.535462764

Break this problem into two subproblems by setting 
(v + 1) equal to 2.535462764 and -2.535462764.

Subproblem 1
v + 1 = 2.535462764

Simplifying
v + 1 = 2.535462764

Reorder the terms:
1 + v = 2.535462764

Solving
1 + v = 2.535462764

Solving for variable 'v'.

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

Add '-1' to each side of the equation.
1 + -1 + v = 2.535462764 + -1

Combine like terms: 1 + -1 = 0
0 + v = 2.535462764 + -1
v = 2.535462764 + -1

Combine like terms: 2.535462764 + -1 = 1.535462764
v = 1.535462764

Simplifying
v = 1.535462764

Subproblem 2
v + 1 = -2.535462764

Simplifying
v + 1 = -2.535462764

Reorder the terms:
1 + v = -2.535462764

Solving
1 + v = -2.535462764

Solving for variable 'v'.

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

Add '-1' to each side of the equation.
1 + -1 + v = -2.535462764 + -1

Combine like terms: 1 + -1 = 0
0 + v = -2.535462764 + -1
v = -2.535462764 + -1

Combine like terms: -2.535462764 + -1 = -3.535462764
v = -3.535462764

Simplifying
v = -3.535462764

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {1.535462764, -3.535462764}