22r^2+22r+4=0

Solution for 22r^2+22r+4=0 equation:

Simplifying
22r2 + 22r + 4 = 0

Reorder the terms:
4 + 22r + 22r2 = 0

Solving
4 + 22r + 22r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 11r + 11r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 11r + 11r2)' equal to zero and attempt to solve:

Simplifying
2 + 11r + 11r2 = 0

Solving
2 + 11r + 11r2 = 0

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

Divide each side by '11'.
0.1818181818 + r + r2 = 0

Move the constant term to the right:

Add '-0.1818181818' to each side of the equation.
0.1818181818 + r + -0.1818181818 + r2 = 0 + -0.1818181818

Reorder the terms:
0.1818181818 + -0.1818181818 + r + r2 = 0 + -0.1818181818

Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000
0.0000000000 + r + r2 = 0 + -0.1818181818
r + r2 = 0 + -0.1818181818

Combine like terms: 0 + -0.1818181818 = -0.1818181818
r + r2 = -0.1818181818

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + r2 = -0.1818181818 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + r2 = -0.1818181818 + 0.25

Combine like terms: -0.1818181818 + 0.25 = 0.0681818182
1.25 + r2 = 0.0681818182

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 0.0681818182

Calculate the square root of the right side: 0.261116484

Break this problem into two subproblems by setting 
(r + 0.5) equal to 0.261116484 and -0.261116484.

Subproblem 1
r + 0.5 = 0.261116484

Simplifying
r + 0.5 = 0.261116484

Reorder the terms:
0.5 + r = 0.261116484

Solving
0.5 + r = 0.261116484

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 0.261116484 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 0.261116484 + -0.5
r = 0.261116484 + -0.5

Combine like terms: 0.261116484 + -0.5 = -0.238883516
r = -0.238883516

Simplifying
r = -0.238883516

Subproblem 2
r + 0.5 = -0.261116484

Simplifying
r + 0.5 = -0.261116484

Reorder the terms:
0.5 + r = -0.261116484

Solving
0.5 + r = -0.261116484

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -0.261116484 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -0.261116484 + -0.5
r = -0.261116484 + -0.5

Combine like terms: -0.261116484 + -0.5 = -0.761116484
r = -0.761116484

Simplifying
r = -0.761116484

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.238883516, -0.761116484}
Solution
r = {-0.238883516, -0.761116484}