n^2+9n-2000=0

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Solution for n^2+9n-2000=0 equation: 


Simplifying
n2 + 9n + -2000 = 0

Reorder the terms:
-2000 + 9n + n2 = 0

Solving
-2000 + 9n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + 9n + 2000 + n2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + 9n + n2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + 9n + n2 = 0 + 2000
9n + n2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
9n + n2 = 2000

The n term is 9n.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9n + 20.25 + n2 = 2000 + 20.25

Reorder the terms:
20.25 + 9n + n2 = 2000 + 20.25

Combine like terms: 2000 + 20.25 = 2020.25
20.25 + 9n + n2 = 2020.25

Factor a perfect square on the left side:
(n + 4.5)(n + 4.5) = 2020.25

Calculate the square root of the right side: 44.947191236

Break this problem into two subproblems by setting 
(n + 4.5) equal to 44.947191236 and -44.947191236.


Subproblem 1
n + 4.5 = 44.947191236

Simplifying
n + 4.5 = 44.947191236

Reorder the terms:
4.5 + n = 44.947191236

Solving
4.5 + n = 44.947191236

Solving for variable 'n'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + n = 44.947191236 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + n = 44.947191236 + -4.5
n = 44.947191236 + -4.5

Combine like terms: 44.947191236 + -4.5 = 40.447191236
n = 40.447191236

Simplifying
n = 40.447191236


Subproblem 2
n + 4.5 = -44.947191236

Simplifying
n + 4.5 = -44.947191236

Reorder the terms:
4.5 + n = -44.947191236

Solving
4.5 + n = -44.947191236

Solving for variable 'n'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + n = -44.947191236 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + n = -44.947191236 + -4.5
n = -44.947191236 + -4.5

Combine like terms: -44.947191236 + -4.5 = -49.447191236
n = -49.447191236

Simplifying
n = -49.447191236


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {40.447191236, -49.447191236}

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