n^2+2n-1000=0

Solution for n^2+2n-1000=0 equation:

Simplifying
n2 + 2n + -1000 = 0

Reorder the terms:
-1000 + 2n + n2 = 0

Solving
-1000 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 2n + 1000 + n2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 2n + n2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 2n + n2 = 0 + 1000
2n + n2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
2n + n2 = 1000

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 1000 + 1

Reorder the terms:
1 + 2n + n2 = 1000 + 1

Combine like terms: 1000 + 1 = 1001
1 + 2n + n2 = 1001

Factor a perfect square on the left side:
(n + 1)(n + 1) = 1001

Calculate the square root of the right side: 31.638584039

Break this problem into two subproblems by setting 
(n + 1) equal to 31.638584039 and -31.638584039.

Subproblem 1
n + 1 = 31.638584039

Simplifying
n + 1 = 31.638584039

Reorder the terms:
1 + n = 31.638584039

Solving
1 + n = 31.638584039

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 31.638584039 + -1

Combine like terms: 1 + -1 = 0
0 + n = 31.638584039 + -1
n = 31.638584039 + -1

Combine like terms: 31.638584039 + -1 = 30.638584039
n = 30.638584039

Simplifying
n = 30.638584039

Subproblem 2
n + 1 = -31.638584039

Simplifying
n + 1 = -31.638584039

Reorder the terms:
1 + n = -31.638584039

Solving
1 + n = -31.638584039

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -31.638584039 + -1

Combine like terms: 1 + -1 = 0
0 + n = -31.638584039 + -1
n = -31.638584039 + -1

Combine like terms: -31.638584039 + -1 = -32.638584039
n = -32.638584039

Simplifying
n = -32.638584039

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {30.638584039, -32.638584039}