n^2+2n+n=667.95

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


Simplifying
n2 + 2n + n = 667.95

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

Combine like terms: 2n + n = 3n
3n + n2 = 667.95

Solving
3n + n2 = 667.95

Solving for variable 'n'.

Reorder the terms:
-667.95 + 3n + n2 = 667.95 + -667.95

Combine like terms: 667.95 + -667.95 = 0.00
-667.95 + 3n + 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 + 3n + 667.95 + n2 = 0.00 + 667.95

Reorder the terms:
-667.95 + 667.95 + 3n + n2 = 0.00 + 667.95

Combine like terms: -667.95 + 667.95 = 0.00
0.00 + 3n + n2 = 0.00 + 667.95
3n + n2 = 0.00 + 667.95

Combine like terms: 0.00 + 667.95 = 667.95
3n + n2 = 667.95

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 667.95 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 667.95 + 2.25

Combine like terms: 667.95 + 2.25 = 670.2
2.25 + 3n + n2 = 670.2

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 670.2

Calculate the square root of the right side: 25.88822126

Break this problem into two subproblems by setting 
(n + 1.5) equal to 25.88822126 and -25.88822126.


Subproblem 1
n + 1.5 = 25.88822126

Simplifying
n + 1.5 = 25.88822126

Reorder the terms:
1.5 + n = 25.88822126

Solving
1.5 + n = 25.88822126

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = 25.88822126 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 25.88822126 + -1.5
n = 25.88822126 + -1.5

Combine like terms: 25.88822126 + -1.5 = 24.38822126
n = 24.38822126

Simplifying
n = 24.38822126


Subproblem 2
n + 1.5 = -25.88822126

Simplifying
n + 1.5 = -25.88822126

Reorder the terms:
1.5 + n = -25.88822126

Solving
1.5 + n = -25.88822126

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = -25.88822126 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -25.88822126 + -1.5
n = -25.88822126 + -1.5

Combine like terms: -25.88822126 + -1.5 = -27.38822126
n = -27.38822126

Simplifying
n = -27.38822126


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {24.38822126, -27.38822126}

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