0.5k^2+15.5k+15=0

Solution for 0.5k^2+15.5k+15=0 equation:

Simplifying
0.5k2 + 15.5k + 15 = 0

Reorder the terms:
15 + 15.5k + 0.5k2 = 0

Solving
15 + 15.5k + 0.5k2 = 0

Solving for variable 'k'.

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

Divide each side by '0.5'.
30 + 31k + k2 = 0

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 31k + -30 + k2 = 0 + -30

Reorder the terms:
30 + -30 + 31k + k2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 31k + k2 = 0 + -30
31k + k2 = 0 + -30

Combine like terms: 0 + -30 = -30
31k + k2 = -30

The k term is 31k.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31k + 240.25 + k2 = -30 + 240.25

Reorder the terms:
240.25 + 31k + k2 = -30 + 240.25

Combine like terms: -30 + 240.25 = 210.25
240.25 + 31k + k2 = 210.25

Factor a perfect square on the left side:
(k + 15.5)(k + 15.5) = 210.25

Calculate the square root of the right side: 14.5

Break this problem into two subproblems by setting 
(k + 15.5) equal to 14.5 and -14.5.

Subproblem 1
k + 15.5 = 14.5

Simplifying
k + 15.5 = 14.5

Reorder the terms:
15.5 + k = 14.5

Solving
15.5 + k = 14.5

Solving for variable 'k'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + k = 14.5 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + k = 14.5 + -15.5
k = 14.5 + -15.5

Combine like terms: 14.5 + -15.5 = -1
k = -1

Simplifying
k = -1

Subproblem 2
k + 15.5 = -14.5

Simplifying
k + 15.5 = -14.5

Reorder the terms:
15.5 + k = -14.5

Solving
15.5 + k = -14.5

Solving for variable 'k'.

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

Add '-15.5' to each side of the equation.
15.5 + -15.5 + k = -14.5 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + k = -14.5 + -15.5
k = -14.5 + -15.5

Combine like terms: -14.5 + -15.5 = -30
k = -30

Simplifying
k = -30

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {-1, -30}