N(N+1)=1200

Solution for N(N+1)=1200 equation:

Simplifying
N(N + 1) = 1200

Reorder the terms:
N(1 + N) = 1200
(1 * N + N * N) = 1200
(1N + N2) = 1200

Solving
1N + N2 = 1200

Solving for variable 'N'.

Reorder the terms:
-1200 + 1N + N2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
-1200 + 1N + N2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1200' to each side of the equation.
-1200 + 1N + 1200 + N2 = 0 + 1200

Reorder the terms:
-1200 + 1200 + 1N + N2 = 0 + 1200

Combine like terms: -1200 + 1200 = 0
0 + 1N + N2 = 0 + 1200
1N + N2 = 0 + 1200

Combine like terms: 0 + 1200 = 1200
1N + N2 = 1200

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.
N + 0.25 + N2 = 1200 + 0.25

Reorder the terms:
0.25 + N + N2 = 1200 + 0.25

Combine like terms: 1200 + 0.25 = 1200.25
0.25 + N + N2 = 1200.25

Factor a perfect square on the left side:
(N + 0.5)(N + 0.5) = 1200.25

Calculate the square root of the right side: 34.644624403

Break this problem into two subproblems by setting 
(N + 0.5) equal to 34.644624403 and -34.644624403.

Subproblem 1
N + 0.5 = 34.644624403

Simplifying
N + 0.5 = 34.644624403

Reorder the terms:
0.5 + N = 34.644624403

Solving
0.5 + N = 34.644624403

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 = 34.644624403 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + N = 34.644624403 + -0.5
N = 34.644624403 + -0.5

Combine like terms: 34.644624403 + -0.5 = 34.144624403
N = 34.144624403

Simplifying
N = 34.144624403

Subproblem 2
N + 0.5 = -34.644624403

Simplifying
N + 0.5 = -34.644624403

Reorder the terms:
0.5 + N = -34.644624403

Solving
0.5 + N = -34.644624403

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 = -34.644624403 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + N = -34.644624403 + -0.5
N = -34.644624403 + -0.5

Combine like terms: -34.644624403 + -0.5 = -35.144624403
N = -35.144624403

Simplifying
N = -35.144624403

Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {34.144624403, -35.144624403}