2k(k+11)=11

Solution for 2k(k+11)=11 equation:

Simplifying
2k(k + 11) = 11

Reorder the terms:
2k(11 + k) = 11
(11 * 2k + k * 2k) = 11
(22k + 2k2) = 11

Solving
22k + 2k2 = 11

Solving for variable 'k'.

Reorder the terms:
-11 + 22k + 2k2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 22k + 2k2 = 0

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

Divide each side by '2'.
-5.5 + 11k + k2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 11k + 5.5 + k2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 11k + k2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 11k + k2 = 0 + 5.5
11k + k2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
11k + k2 = 5.5

The k term is 11k.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11k + 30.25 + k2 = 5.5 + 30.25

Reorder the terms:
30.25 + 11k + k2 = 5.5 + 30.25

Combine like terms: 5.5 + 30.25 = 35.75
30.25 + 11k + k2 = 35.75

Factor a perfect square on the left side:
(k + 5.5)(k + 5.5) = 35.75

Calculate the square root of the right side: 5.979130372

Break this problem into two subproblems by setting 
(k + 5.5) equal to 5.979130372 and -5.979130372.

Subproblem 1
k + 5.5 = 5.979130372

Simplifying
k + 5.5 = 5.979130372

Reorder the terms:
5.5 + k = 5.979130372

Solving
5.5 + k = 5.979130372

Solving for variable 'k'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + k = 5.979130372 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + k = 5.979130372 + -5.5
k = 5.979130372 + -5.5

Combine like terms: 5.979130372 + -5.5 = 0.479130372
k = 0.479130372

Simplifying
k = 0.479130372

Subproblem 2
k + 5.5 = -5.979130372

Simplifying
k + 5.5 = -5.979130372

Reorder the terms:
5.5 + k = -5.979130372

Solving
5.5 + k = -5.979130372

Solving for variable 'k'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + k = -5.979130372 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + k = -5.979130372 + -5.5
k = -5.979130372 + -5.5

Combine like terms: -5.979130372 + -5.5 = -11.479130372
k = -11.479130372

Simplifying
k = -11.479130372

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.479130372, -11.479130372}