-5v^2-22v-18=0

Solution for -5v^2-22v-18=0 equation:

Simplifying
-5v2 + -22v + -18 = 0

Reorder the terms:
-18 + -22v + -5v2 = 0

Solving
-18 + -22v + -5v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 22v + 5v2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(18 + 22v + 5v2)' equal to zero and attempt to solve:

Simplifying
18 + 22v + 5v2 = 0

Solving
18 + 22v + 5v2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
3.6 + 4.4v + v2 = 0

Move the constant term to the right:

Add '-3.6' to each side of the equation.
3.6 + 4.4v + -3.6 + v2 = 0 + -3.6

Reorder the terms:
3.6 + -3.6 + 4.4v + v2 = 0 + -3.6

Combine like terms: 3.6 + -3.6 = 0.0
0.0 + 4.4v + v2 = 0 + -3.6
4.4v + v2 = 0 + -3.6

Combine like terms: 0 + -3.6 = -3.6
4.4v + v2 = -3.6

The v term is 4.4v.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4v + 4.84 + v2 = -3.6 + 4.84

Reorder the terms:
4.84 + 4.4v + v2 = -3.6 + 4.84

Combine like terms: -3.6 + 4.84 = 1.24
4.84 + 4.4v + v2 = 1.24

Factor a perfect square on the left side:
(v + 2.2)(v + 2.2) = 1.24

Calculate the square root of the right side: 1.113552873

Break this problem into two subproblems by setting 
(v + 2.2) equal to 1.113552873 and -1.113552873.

Subproblem 1
v + 2.2 = 1.113552873

Simplifying
v + 2.2 = 1.113552873

Reorder the terms:
2.2 + v = 1.113552873

Solving
2.2 + v = 1.113552873

Solving for variable 'v'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + v = 1.113552873 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + v = 1.113552873 + -2.2
v = 1.113552873 + -2.2

Combine like terms: 1.113552873 + -2.2 = -1.086447127
v = -1.086447127

Simplifying
v = -1.086447127

Subproblem 2
v + 2.2 = -1.113552873

Simplifying
v + 2.2 = -1.113552873

Reorder the terms:
2.2 + v = -1.113552873

Solving
2.2 + v = -1.113552873

Solving for variable 'v'.

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

Add '-2.2' to each side of the equation.
2.2 + -2.2 + v = -1.113552873 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + v = -1.113552873 + -2.2
v = -1.113552873 + -2.2

Combine like terms: -1.113552873 + -2.2 = -3.313552873
v = -3.313552873

Simplifying
v = -3.313552873

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {-1.086447127, -3.313552873}
Solution
v = {-1.086447127, -3.313552873}