0.5n^2-0.5n=0.083333333

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Solution for 0.5n^2-0.5n=0.083333333 equation: 


Simplifying
0.5n2 + -0.5n = 0.083333333

Reorder the terms:
-0.5n + 0.5n2 = 0.083333333

Solving
-0.5n + 0.5n2 = 0.083333333

Solving for variable 'n'.

Reorder the terms:
-0.083333333 + -0.5n + 0.5n2 = 0.083333333 + -0.083333333

Combine like terms: 0.083333333 + -0.083333333 = 0.000000000
-0.083333333 + -0.5n + 0.5n2 = 0.000000000

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

Divide each side by '0.5'.
-0.166666666 + -1n + n2 = 0.00000000

Move the constant term to the right:

Add '0.166666666' to each side of the equation.
-0.166666666 + -1n + 0.166666666 + n2 = 0.00000000 + 0.166666666

Reorder the terms:
-0.166666666 + 0.166666666 + -1n + n2 = 0.00000000 + 0.166666666

Combine like terms: -0.166666666 + 0.166666666 = 0.000000000
0.000000000 + -1n + n2 = 0.00000000 + 0.166666666
-1n + n2 = 0.00000000 + 0.166666666

Combine like terms: 0.00000000 + 0.166666666 = 0.166666666
-1n + n2 = 0.166666666

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 = 0.166666666 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 0.166666666 + 0.25

Combine like terms: 0.166666666 + 0.25 = 0.416666666
0.25 + -1n + n2 = 0.416666666

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 0.416666666

Calculate the square root of the right side: 0.645497224

Break this problem into two subproblems by setting 
(n + -0.5) equal to 0.645497224 and -0.645497224.


Subproblem 1
n + -0.5 = 0.645497224

Simplifying
n + -0.5 = 0.645497224

Reorder the terms:
-0.5 + n = 0.645497224

Solving
-0.5 + n = 0.645497224

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 = 0.645497224 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 0.645497224 + 0.5
n = 0.645497224 + 0.5

Combine like terms: 0.645497224 + 0.5 = 1.145497224
n = 1.145497224

Simplifying
n = 1.145497224


Subproblem 2
n + -0.5 = -0.645497224

Simplifying
n + -0.5 = -0.645497224

Reorder the terms:
-0.5 + n = -0.645497224

Solving
-0.5 + n = -0.645497224

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 = -0.645497224 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -0.645497224 + 0.5
n = -0.645497224 + 0.5

Combine like terms: -0.645497224 + 0.5 = -0.145497224
n = -0.145497224

Simplifying
n = -0.145497224


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.145497224, -0.145497224}

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