v^2+6v-23=0

Solution for v^2+6v-23=0 equation:

Simplifying
v2 + 6v + -23 = 0

Reorder the terms:
-23 + 6v + v2 = 0

Solving
-23 + 6v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 6v + 23 + v2 = 0 + 23

Reorder the terms:
-23 + 23 + 6v + v2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 6v + v2 = 0 + 23
6v + v2 = 0 + 23

Combine like terms: 0 + 23 = 23
6v + v2 = 23

The v term is 6v.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6v + 9 + v2 = 23 + 9

Reorder the terms:
9 + 6v + v2 = 23 + 9

Combine like terms: 23 + 9 = 32
9 + 6v + v2 = 32

Factor a perfect square on the left side:
(v + 3)(v + 3) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(v + 3) equal to 5.656854249 and -5.656854249.

Subproblem 1
v + 3 = 5.656854249

Simplifying
v + 3 = 5.656854249

Reorder the terms:
3 + v = 5.656854249

Solving
3 + v = 5.656854249

Solving for variable 'v'.

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

Add '-3' to each side of the equation.
3 + -3 + v = 5.656854249 + -3

Combine like terms: 3 + -3 = 0
0 + v = 5.656854249 + -3
v = 5.656854249 + -3

Combine like terms: 5.656854249 + -3 = 2.656854249
v = 2.656854249

Simplifying
v = 2.656854249

Subproblem 2
v + 3 = -5.656854249

Simplifying
v + 3 = -5.656854249

Reorder the terms:
3 + v = -5.656854249

Solving
3 + v = -5.656854249

Solving for variable 'v'.

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

Add '-3' to each side of the equation.
3 + -3 + v = -5.656854249 + -3

Combine like terms: 3 + -3 = 0
0 + v = -5.656854249 + -3
v = -5.656854249 + -3

Combine like terms: -5.656854249 + -3 = -8.656854249
v = -8.656854249

Simplifying
v = -8.656854249

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.656854249, -8.656854249}