n^2+2n-n=667.95

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Solution for n^2+2n-n=667.95 equation: 


Simplifying
n2 + 2n + -1n = 667.95

Reorder the terms:
2n + -1n + n2 = 667.95

Combine like terms: 2n + -1n = 1n
1n + n2 = 667.95

Solving
1n + n2 = 667.95

Solving for variable 'n'.

Reorder the terms:
-667.95 + 1n + n2 = 667.95 + -667.95

Combine like terms: 667.95 + -667.95 = 0.00
-667.95 + 1n + n2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '667.95' to each side of the equation.
-667.95 + 1n + 667.95 + n2 = 0.00 + 667.95

Reorder the terms:
-667.95 + 667.95 + 1n + n2 = 0.00 + 667.95

Combine like terms: -667.95 + 667.95 = 0.00
0.00 + 1n + n2 = 0.00 + 667.95
1n + n2 = 0.00 + 667.95

Combine like terms: 0.00 + 667.95 = 667.95
1n + n2 = 667.95

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.
n + 0.25 + n2 = 667.95 + 0.25

Reorder the terms:
0.25 + n + n2 = 667.95 + 0.25

Combine like terms: 667.95 + 0.25 = 668.2
0.25 + n + n2 = 668.2

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 668.2

Calculate the square root of the right side: 25.849564793

Break this problem into two subproblems by setting 
(n + 0.5) equal to 25.849564793 and -25.849564793.


Subproblem 1
n + 0.5 = 25.849564793

Simplifying
n + 0.5 = 25.849564793

Reorder the terms:
0.5 + n = 25.849564793

Solving
0.5 + n = 25.849564793

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 = 25.849564793 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 25.849564793 + -0.5
n = 25.849564793 + -0.5

Combine like terms: 25.849564793 + -0.5 = 25.349564793
n = 25.349564793

Simplifying
n = 25.349564793


Subproblem 2
n + 0.5 = -25.849564793

Simplifying
n + 0.5 = -25.849564793

Reorder the terms:
0.5 + n = -25.849564793

Solving
0.5 + n = -25.849564793

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 = -25.849564793 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -25.849564793 + -0.5
n = -25.849564793 + -0.5

Combine like terms: -25.849564793 + -0.5 = -26.349564793
n = -26.349564793

Simplifying
n = -26.349564793


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {25.349564793, -26.349564793}

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