n(n+2)=2862

Solution for n(n+2)=2862 equation:

Simplifying
n(n + 2) = 2862

Reorder the terms:
n(2 + n) = 2862
(2 * n + n * n) = 2862
(2n + n2) = 2862

Solving
2n + n2 = 2862

Solving for variable 'n'.

Reorder the terms:
-2862 + 2n + n2 = 2862 + -2862

Combine like terms: 2862 + -2862 = 0
-2862 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2862' to each side of the equation.
-2862 + 2n + 2862 + n2 = 0 + 2862

Reorder the terms:
-2862 + 2862 + 2n + n2 = 0 + 2862

Combine like terms: -2862 + 2862 = 0
0 + 2n + n2 = 0 + 2862
2n + n2 = 0 + 2862

Combine like terms: 0 + 2862 = 2862
2n + n2 = 2862

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 = 2862 + 1

Reorder the terms:
1 + 2n + n2 = 2862 + 1

Combine like terms: 2862 + 1 = 2863
1 + 2n + n2 = 2863

Factor a perfect square on the left side:
(n + 1)(n + 1) = 2863

Calculate the square root of the right side: 53.507008887

Break this problem into two subproblems by setting 
(n + 1) equal to 53.507008887 and -53.507008887.

Subproblem 1
n + 1 = 53.507008887

Simplifying
n + 1 = 53.507008887

Reorder the terms:
1 + n = 53.507008887

Solving
1 + n = 53.507008887

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 = 53.507008887 + -1

Combine like terms: 1 + -1 = 0
0 + n = 53.507008887 + -1
n = 53.507008887 + -1

Combine like terms: 53.507008887 + -1 = 52.507008887
n = 52.507008887

Simplifying
n = 52.507008887

Subproblem 2
n + 1 = -53.507008887

Simplifying
n + 1 = -53.507008887

Reorder the terms:
1 + n = -53.507008887

Solving
1 + n = -53.507008887

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 = -53.507008887 + -1

Combine like terms: 1 + -1 = 0
0 + n = -53.507008887 + -1
n = -53.507008887 + -1

Combine like terms: -53.507008887 + -1 = -54.507008887
n = -54.507008887

Simplifying
n = -54.507008887

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {52.507008887, -54.507008887}