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 + n + n2 = 0.00000000

Move the constant term to the right:

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

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

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

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

The n term is n.  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.
 + 0.25 + n2 = -0.166666666 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = -0.166666666 + 0.25

Combine like terms: -0.166666666 + 0.25 = 0.083333334
1.25 + n2 = 0.083333334

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 0.083333334

Calculate the square root of the right side: 0.288675136

Break this problem into two subproblems by setting 
(n + 0.5) equal to 0.288675136 and -0.288675136.


Subproblem 1
n + 0.5 = 0.288675136

Simplifying
n + 0.5 = 0.288675136

Reorder the terms:
0.5 + n = 0.288675136

Solving
0.5 + n = 0.288675136

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 = 0.288675136 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 0.288675136 + -0.5
n = 0.288675136 + -0.5

Combine like terms: 0.288675136 + -0.5 = -0.211324864
n = -0.211324864

Simplifying
n = -0.211324864


Subproblem 2
n + 0.5 = -0.288675136

Simplifying
n + 0.5 = -0.288675136

Reorder the terms:
0.5 + n = -0.288675136

Solving
0.5 + n = -0.288675136

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 = -0.288675136 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -0.288675136 + -0.5
n = -0.288675136 + -0.5

Combine like terms: -0.288675136 + -0.5 = -0.788675136
n = -0.788675136

Simplifying
n = -0.788675136


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.211324864, -0.788675136}

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