2r^2+24r+11=0

Solution for 2r^2+24r+11=0 equation:

Simplifying
2r2 + 24r + 11 = 0

Reorder the terms:
11 + 24r + 2r2 = 0

Solving
11 + 24r + 2r2 = 0

Solving for variable 'r'.

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

Divide each side by '2'.
5.5 + 12r + r2 = 0

Move the constant term to the right:

Add '-5.5' to each side of the equation.
5.5 + 12r + -5.5 + r2 = 0 + -5.5

Reorder the terms:
5.5 + -5.5 + 12r + r2 = 0 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + 12r + r2 = 0 + -5.5
12r + r2 = 0 + -5.5

Combine like terms: 0 + -5.5 = -5.5
12r + r2 = -5.5

The r term is 12r.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12r + 36 + r2 = -5.5 + 36

Reorder the terms:
36 + 12r + r2 = -5.5 + 36

Combine like terms: -5.5 + 36 = 30.5
36 + 12r + r2 = 30.5

Factor a perfect square on the left side:
(r + 6)(r + 6) = 30.5

Calculate the square root of the right side: 5.522680509

Break this problem into two subproblems by setting 
(r + 6) equal to 5.522680509 and -5.522680509.

Subproblem 1
r + 6 = 5.522680509

Simplifying
r + 6 = 5.522680509

Reorder the terms:
6 + r = 5.522680509

Solving
6 + r = 5.522680509

Solving for variable 'r'.

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

Add '-6' to each side of the equation.
6 + -6 + r = 5.522680509 + -6

Combine like terms: 6 + -6 = 0
0 + r = 5.522680509 + -6
r = 5.522680509 + -6

Combine like terms: 5.522680509 + -6 = -0.477319491
r = -0.477319491

Simplifying
r = -0.477319491

Subproblem 2
r + 6 = -5.522680509

Simplifying
r + 6 = -5.522680509

Reorder the terms:
6 + r = -5.522680509

Solving
6 + r = -5.522680509

Solving for variable 'r'.

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

Add '-6' to each side of the equation.
6 + -6 + r = -5.522680509 + -6

Combine like terms: 6 + -6 = 0
0 + r = -5.522680509 + -6
r = -5.522680509 + -6

Combine like terms: -5.522680509 + -6 = -11.522680509
r = -11.522680509

Simplifying
r = -11.522680509

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.477319491, -11.522680509}