v^2+2v-32=0

Solution for v^2+2v-32=0 equation:

Simplifying
v2 + 2v + -32 = 0

Reorder the terms:
-32 + 2v + v2 = 0

Solving
-32 + 2v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 2v + 32 + v2 = 0 + 32

Reorder the terms:
-32 + 32 + 2v + v2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 2v + v2 = 0 + 32
2v + v2 = 0 + 32

Combine like terms: 0 + 32 = 32
2v + v2 = 32

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 = 32 + 1

Reorder the terms:
1 + 2v + v2 = 32 + 1

Combine like terms: 32 + 1 = 33
1 + 2v + v2 = 33

Factor a perfect square on the left side:
(v + 1)(v + 1) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(v + 1) equal to 5.744562647 and -5.744562647.

Subproblem 1
v + 1 = 5.744562647

Simplifying
v + 1 = 5.744562647

Reorder the terms:
1 + v = 5.744562647

Solving
1 + v = 5.744562647

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 = 5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + v = 5.744562647 + -1
v = 5.744562647 + -1

Combine like terms: 5.744562647 + -1 = 4.744562647
v = 4.744562647

Simplifying
v = 4.744562647

Subproblem 2
v + 1 = -5.744562647

Simplifying
v + 1 = -5.744562647

Reorder the terms:
1 + v = -5.744562647

Solving
1 + v = -5.744562647

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 = -5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + v = -5.744562647 + -1
v = -5.744562647 + -1

Combine like terms: -5.744562647 + -1 = -6.744562647
v = -6.744562647

Simplifying
v = -6.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {4.744562647, -6.744562647}