v^2+8v+9=0

Solution for v^2+8v+9=0 equation:

Simplifying
v2 + 8v + 9 = 0

Reorder the terms:
9 + 8v + v2 = 0

Solving
9 + 8v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8v + -9 + v2 = 0 + -9

Reorder the terms:
9 + -9 + 8v + v2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8v + v2 = 0 + -9
8v + v2 = 0 + -9

Combine like terms: 0 + -9 = -9
8v + v2 = -9

The v term is 8v.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8v + 16 + v2 = -9 + 16

Reorder the terms:
16 + 8v + v2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + 8v + v2 = 7

Factor a perfect square on the left side:
(v + 4)(v + 4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(v + 4) equal to 2.645751311 and -2.645751311.

Subproblem 1
v + 4 = 2.645751311

Simplifying
v + 4 = 2.645751311

Reorder the terms:
4 + v = 2.645751311

Solving
4 + v = 2.645751311

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = 2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + v = 2.645751311 + -4
v = 2.645751311 + -4

Combine like terms: 2.645751311 + -4 = -1.354248689
v = -1.354248689

Simplifying
v = -1.354248689

Subproblem 2
v + 4 = -2.645751311

Simplifying
v + 4 = -2.645751311

Reorder the terms:
4 + v = -2.645751311

Solving
4 + v = -2.645751311

Solving for variable 'v'.

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

Add '-4' to each side of the equation.
4 + -4 + v = -2.645751311 + -4

Combine like terms: 4 + -4 = 0
0 + v = -2.645751311 + -4
v = -2.645751311 + -4

Combine like terms: -2.645751311 + -4 = -6.645751311
v = -6.645751311

Simplifying
v = -6.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-1.354248689, -6.645751311}