v^2+2v-14=0

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

Simplifying
v2 + 2v + -14 = 0

Reorder the terms:
-14 + 2v + v2 = 0

Solving
-14 + 2v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 2v + 14 + v2 = 0 + 14

Reorder the terms:
-14 + 14 + 2v + v2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 2v + v2 = 0 + 14
2v + v2 = 0 + 14

Combine like terms: 0 + 14 = 14
2v + v2 = 14

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 = 14 + 1

Reorder the terms:
1 + 2v + v2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + 2v + v2 = 15

Factor a perfect square on the left side:
(v + 1)(v + 1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(v + 1) equal to 3.872983346 and -3.872983346.

Subproblem 1
v + 1 = 3.872983346

Simplifying
v + 1 = 3.872983346

Reorder the terms:
1 + v = 3.872983346

Solving
1 + v = 3.872983346

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 = 3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + v = 3.872983346 + -1
v = 3.872983346 + -1

Combine like terms: 3.872983346 + -1 = 2.872983346
v = 2.872983346

Simplifying
v = 2.872983346

Subproblem 2
v + 1 = -3.872983346

Simplifying
v + 1 = -3.872983346

Reorder the terms:
1 + v = -3.872983346

Solving
1 + v = -3.872983346

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 = -3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + v = -3.872983346 + -1
v = -3.872983346 + -1

Combine like terms: -3.872983346 + -1 = -4.872983346
v = -4.872983346

Simplifying
v = -4.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.872983346, -4.872983346}