11k^2-5k=2

Solution for 11k^2-5k=2 equation:

Simplifying
11k2 + -5k = 2

Reorder the terms:
-5k + 11k2 = 2

Solving
-5k + 11k2 = 2

Solving for variable 'k'.

Reorder the terms:
-2 + -5k + 11k2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -5k + 11k2 = 0

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

Divide each side by '11'.
-0.1818181818 + -0.4545454545k + k2 = 0

Move the constant term to the right:

Add '0.1818181818' to each side of the equation.
-0.1818181818 + -0.4545454545k + 0.1818181818 + k2 = 0 + 0.1818181818

Reorder the terms:
-0.1818181818 + 0.1818181818 + -0.4545454545k + k2 = 0 + 0.1818181818

Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000
0.0000000000 + -0.4545454545k + k2 = 0 + 0.1818181818
-0.4545454545k + k2 = 0 + 0.1818181818

Combine like terms: 0 + 0.1818181818 = 0.1818181818
-0.4545454545k + k2 = 0.1818181818

The k term is -0.4545454545k.  Take half its coefficient (-0.2272727273).
Square it (0.05165289257) and add it to both sides.

Add '0.05165289257' to each side of the equation.
-0.4545454545k + 0.05165289257 + k2 = 0.1818181818 + 0.05165289257

Reorder the terms:
0.05165289257 + -0.4545454545k + k2 = 0.1818181818 + 0.05165289257

Combine like terms: 0.1818181818 + 0.05165289257 = 0.23347107437
0.05165289257 + -0.4545454545k + k2 = 0.23347107437

Factor a perfect square on the left side:
(k + -0.2272727273)(k + -0.2272727273) = 0.23347107437

Calculate the square root of the right side: 0.483188446

Break this problem into two subproblems by setting 
(k + -0.2272727273) equal to 0.483188446 and -0.483188446.

Subproblem 1
k + -0.2272727273 = 0.483188446

Simplifying
k + -0.2272727273 = 0.483188446

Reorder the terms:
-0.2272727273 + k = 0.483188446

Solving
-0.2272727273 + k = 0.483188446

Solving for variable 'k'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + k = 0.483188446 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + k = 0.483188446 + 0.2272727273
k = 0.483188446 + 0.2272727273

Combine like terms: 0.483188446 + 0.2272727273 = 0.7104611733
k = 0.7104611733

Simplifying
k = 0.7104611733

Subproblem 2
k + -0.2272727273 = -0.483188446

Simplifying
k + -0.2272727273 = -0.483188446

Reorder the terms:
-0.2272727273 + k = -0.483188446

Solving
-0.2272727273 + k = -0.483188446

Solving for variable 'k'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + k = -0.483188446 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + k = -0.483188446 + 0.2272727273
k = -0.483188446 + 0.2272727273

Combine like terms: -0.483188446 + 0.2272727273 = -0.2559157187
k = -0.2559157187

Simplifying
k = -0.2559157187

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.7104611733, -0.2559157187}