11k+2=k^2

Solution for 11k+2=k^2 equation:

Simplifying
11k + 2 = k2

Reorder the terms:
2 + 11k = k2

Solving
2 + 11k = k2

Solving for variable 'k'.

Combine like terms: k2 + -1k2 = 0
2 + 11k + -1k2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -11k + k2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -11k + 2 + k2 = 0 + 2

Reorder the terms:
-2 + 2 + -11k + k2 = 0 + 2

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

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

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 = 2 + 30.25

Reorder the terms:
30.25 + -11k + k2 = 2 + 30.25

Combine like terms: 2 + 30.25 = 32.25
30.25 + -11k + k2 = 32.25

Factor a perfect square on the left side:
(k + -5.5)(k + -5.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(k + -5.5) equal to 5.678908346 and -5.678908346.

Subproblem 1
k + -5.5 = 5.678908346

Simplifying
k + -5.5 = 5.678908346

Reorder the terms:
-5.5 + k = 5.678908346

Solving
-5.5 + k = 5.678908346

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 = 5.678908346 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + k = 5.678908346 + 5.5
k = 5.678908346 + 5.5

Combine like terms: 5.678908346 + 5.5 = 11.178908346
k = 11.178908346

Simplifying
k = 11.178908346

Subproblem 2
k + -5.5 = -5.678908346

Simplifying
k + -5.5 = -5.678908346

Reorder the terms:
-5.5 + k = -5.678908346

Solving
-5.5 + k = -5.678908346

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 = -5.678908346 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + k = -5.678908346 + 5.5
k = -5.678908346 + 5.5

Combine like terms: -5.678908346 + 5.5 = -0.178908346
k = -0.178908346

Simplifying
k = -0.178908346

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {11.178908346, -0.178908346}