n(n-1)=2000

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Solution for n(n-1)=2000 equation: 


Simplifying
n(n + -1) = 2000

Reorder the terms:
n(-1 + n) = 2000
(-1 * n + n * n) = 2000
(-1n + n2) = 2000

Solving
-1n + n2 = 2000

Solving for variable 'n'.

Reorder the terms:
-2000 + -1n + n2 = 2000 + -2000

Combine like terms: 2000 + -2000 = 0
-2000 + -1n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + -1n + 2000 + n2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + -1n + n2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + -1n + n2 = 0 + 2000
-1n + n2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
-1n + n2 = 2000

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 = 2000 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 2000 + 0.25

Combine like terms: 2000 + 0.25 = 2000.25
0.25 + -1n + n2 = 2000.25

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 2000.25

Calculate the square root of the right side: 44.724154548

Break this problem into two subproblems by setting 
(n + -0.5) equal to 44.724154548 and -44.724154548.


Subproblem 1
n + -0.5 = 44.724154548

Simplifying
n + -0.5 = 44.724154548

Reorder the terms:
-0.5 + n = 44.724154548

Solving
-0.5 + n = 44.724154548

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 = 44.724154548 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 44.724154548 + 0.5
n = 44.724154548 + 0.5

Combine like terms: 44.724154548 + 0.5 = 45.224154548
n = 45.224154548

Simplifying
n = 45.224154548


Subproblem 2
n + -0.5 = -44.724154548

Simplifying
n + -0.5 = -44.724154548

Reorder the terms:
-0.5 + n = -44.724154548

Solving
-0.5 + n = -44.724154548

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 = -44.724154548 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -44.724154548 + 0.5
n = -44.724154548 + 0.5

Combine like terms: -44.724154548 + 0.5 = -44.224154548
n = -44.224154548

Simplifying
n = -44.224154548


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {45.224154548, -44.224154548}

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