0.5n^2-0.5n-15=0

Solution for 0.5n^2-0.5n-15=0 equation:

Simplifying
0.5n2 + -0.5n + -15 = 0

Reorder the terms:
-15 + -0.5n + 0.5n2 = 0

Solving
-15 + -0.5n + 0.5n2 = 0

Solving for variable 'n'.

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

Divide each side by '0.5'.
-30 + -1n + n2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -1n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + -1n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -1n + n2 = 0 + 30
-1n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
-1n + n2 = 30

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 30 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 30 + 0.25

Combine like terms: 30 + 0.25 = 30.25
0.25 + -1n + n2 = 30.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 30.25

Calculate the square root of the right side: 5.5

Break this problem into two subproblems by setting 
(n + -0.5) equal to 5.5 and -5.5.

Subproblem 1
n + -0.5 = 5.5

Simplifying
n + -0.5 = 5.5

Reorder the terms:
-0.5 + n = 5.5

Solving
-0.5 + n = 5.5

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 5.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 5.5 + 0.5
n = 5.5 + 0.5

Combine like terms: 5.5 + 0.5 = 6
n = 6

Simplifying
n = 6

Subproblem 2
n + -0.5 = -5.5

Simplifying
n + -0.5 = -5.5

Reorder the terms:
-0.5 + n = -5.5

Solving
-0.5 + n = -5.5

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -5.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -5.5 + 0.5
n = -5.5 + 0.5

Combine like terms: -5.5 + 0.5 = -5
n = -5

Simplifying
n = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6, -5}