v^2+2v-1=0

Solution for v^2+2v-1=0 equation:

Simplifying
v2 + 2v + -1 = 0

Reorder the terms:
-1 + 2v + v2 = 0

Solving
-1 + 2v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + 2v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2v + v2 = 0 + 1
2v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
2v + v2 = 1

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 = 1 + 1

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

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

Factor a perfect square on the left side:
(v + 1)(v + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(v + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
v + 1 = 1.414213562

Simplifying
v + 1 = 1.414213562

Reorder the terms:
1 + v = 1.414213562

Solving
1 + v = 1.414213562

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 = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + v = 1.414213562 + -1
v = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
v = 0.414213562

Simplifying
v = 0.414213562

Subproblem 2
v + 1 = -1.414213562

Simplifying
v + 1 = -1.414213562

Reorder the terms:
1 + v = -1.414213562

Solving
1 + v = -1.414213562

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 = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + v = -1.414213562 + -1
v = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
v = -2.414213562

Simplifying
v = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.414213562, -2.414213562}