0.5*n^2-0.5*n-60=0

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Solution for 0.5*n^2-0.5*n-60=0 equation: 


Simplifying
0.5n2 + -0.5n + -60 = 0

Reorder the terms:
-60 + -0.5n + 0.5n2 = 0

Solving
-60 + -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'.
-120 + -1n + n2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -1n + 120 + n2 = 0 + 120

Reorder the terms:
-120 + 120 + -1n + n2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -1n + n2 = 0 + 120
-1n + n2 = 0 + 120

Combine like terms: 0 + 120 = 120
-1n + n2 = 120

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 = 120 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 120 + 0.25

Combine like terms: 120 + 0.25 = 120.25
0.25 + -1n + n2 = 120.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(n + -0.5) equal to 10.9658561 and -10.9658561.


Subproblem 1
n + -0.5 = 10.9658561

Simplifying
n + -0.5 = 10.9658561

Reorder the terms:
-0.5 + n = 10.9658561

Solving
-0.5 + n = 10.9658561

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 = 10.9658561 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 10.9658561 + 0.5
n = 10.9658561 + 0.5

Combine like terms: 10.9658561 + 0.5 = 11.4658561
n = 11.4658561

Simplifying
n = 11.4658561


Subproblem 2
n + -0.5 = -10.9658561

Simplifying
n + -0.5 = -10.9658561

Reorder the terms:
-0.5 + n = -10.9658561

Solving
-0.5 + n = -10.9658561

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 = -10.9658561 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -10.9658561 + 0.5
n = -10.9658561 + 0.5

Combine like terms: -10.9658561 + 0.5 = -10.4658561
n = -10.4658561

Simplifying
n = -10.4658561


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {11.4658561, -10.4658561}

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