5k^2+16k-11=0

Solution for 5k^2+16k-11=0 equation:

Simplifying
5k2 + 16k + -11 = 0

Reorder the terms:
-11 + 16k + 5k2 = 0

Solving
-11 + 16k + 5k2 = 0

Solving for variable 'k'.

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

Divide each side by '5'.
-2.2 + 3.2k + k2 = 0

Move the constant term to the right:

Add '2.2' to each side of the equation.
-2.2 + 3.2k + 2.2 + k2 = 0 + 2.2

Reorder the terms:
-2.2 + 2.2 + 3.2k + k2 = 0 + 2.2

Combine like terms: -2.2 + 2.2 = 0.0
0.0 + 3.2k + k2 = 0 + 2.2
3.2k + k2 = 0 + 2.2

Combine like terms: 0 + 2.2 = 2.2
3.2k + k2 = 2.2

The k term is 3.2k.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2k + 2.56 + k2 = 2.2 + 2.56

Reorder the terms:
2.56 + 3.2k + k2 = 2.2 + 2.56

Combine like terms: 2.2 + 2.56 = 4.76
2.56 + 3.2k + k2 = 4.76

Factor a perfect square on the left side:
(k + 1.6)(k + 1.6) = 4.76

Calculate the square root of the right side: 2.181742423

Break this problem into two subproblems by setting 
(k + 1.6) equal to 2.181742423 and -2.181742423.

Subproblem 1
k + 1.6 = 2.181742423

Simplifying
k + 1.6 = 2.181742423

Reorder the terms:
1.6 + k = 2.181742423

Solving
1.6 + k = 2.181742423

Solving for variable 'k'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + k = 2.181742423 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + k = 2.181742423 + -1.6
k = 2.181742423 + -1.6

Combine like terms: 2.181742423 + -1.6 = 0.581742423
k = 0.581742423

Simplifying
k = 0.581742423

Subproblem 2
k + 1.6 = -2.181742423

Simplifying
k + 1.6 = -2.181742423

Reorder the terms:
1.6 + k = -2.181742423

Solving
1.6 + k = -2.181742423

Solving for variable 'k'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + k = -2.181742423 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + k = -2.181742423 + -1.6
k = -2.181742423 + -1.6

Combine like terms: -2.181742423 + -1.6 = -3.781742423
k = -3.781742423

Simplifying
k = -3.781742423

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.581742423, -3.781742423}