5k^2+11k-162=0

Solution for 5k^2+11k-162=0 equation:

Simplifying
5k2 + 11k + -162 = 0

Reorder the terms:
-162 + 11k + 5k2 = 0

Solving
-162 + 11k + 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'.
-32.4 + 2.2k + k2 = 0

Move the constant term to the right:

Add '32.4' to each side of the equation.
-32.4 + 2.2k + 32.4 + k2 = 0 + 32.4

Reorder the terms:
-32.4 + 32.4 + 2.2k + k2 = 0 + 32.4

Combine like terms: -32.4 + 32.4 = 0.0
0.0 + 2.2k + k2 = 0 + 32.4
2.2k + k2 = 0 + 32.4

Combine like terms: 0 + 32.4 = 32.4
2.2k + k2 = 32.4

The k term is 2.2k.  Take half its coefficient (1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
2.2k + 1.21 + k2 = 32.4 + 1.21

Reorder the terms:
1.21 + 2.2k + k2 = 32.4 + 1.21

Combine like terms: 32.4 + 1.21 = 33.61
1.21 + 2.2k + k2 = 33.61

Factor a perfect square on the left side:
(k + 1.1)(k + 1.1) = 33.61

Calculate the square root of the right side: 5.797413216

Break this problem into two subproblems by setting 
(k + 1.1) equal to 5.797413216 and -5.797413216.

Subproblem 1
k + 1.1 = 5.797413216

Simplifying
k + 1.1 = 5.797413216

Reorder the terms:
1.1 + k = 5.797413216

Solving
1.1 + k = 5.797413216

Solving for variable 'k'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + k = 5.797413216 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + k = 5.797413216 + -1.1
k = 5.797413216 + -1.1

Combine like terms: 5.797413216 + -1.1 = 4.697413216
k = 4.697413216

Simplifying
k = 4.697413216

Subproblem 2
k + 1.1 = -5.797413216

Simplifying
k + 1.1 = -5.797413216

Reorder the terms:
1.1 + k = -5.797413216

Solving
1.1 + k = -5.797413216

Solving for variable 'k'.

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

Add '-1.1' to each side of the equation.
1.1 + -1.1 + k = -5.797413216 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + k = -5.797413216 + -1.1
k = -5.797413216 + -1.1

Combine like terms: -5.797413216 + -1.1 = -6.897413216
k = -6.897413216

Simplifying
k = -6.897413216

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.697413216, -6.897413216}