n(n+1)=2000

Simple and best practice solution for n(n+1)=2000 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

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.
n + 0.25 + n2 = 2000 + 0.25

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

Combine like terms: 2000 + 0.25 = 2000.25
0.25 + n + 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 = 44.224154548 n = 44.224154548 Simplifying n = 44.224154548

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 = -45.224154548 n = -45.224154548 Simplifying n = -45.224154548

Solution

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

See similar equations:

| 14=w+6/9 | | -x+2=-12+6x | | 33y=8(4y-5) | | 3(7+2x)=9x+6 | | x^2+y^2-12x+33=0 | | 10=4+m/7 | | 7(1)+7(-1)=-7 | | 38=2(7-3r)+2(1-8r) | | 10y=9(y+5) | | 10+2=1d | | 39.99+.45n=44.99+.409 | | 5x-9=5x-9 | | -3(2x-5)-x+1=-47 | | 5x-6=71-6x | | -4-6=4x+8-3x | | -8(2b-3)-8(1+5b)=72 | | -67=6t-1 | | b/2-b-5/4=9/4 | | x+y+50=0 | | d-14.25=-32.9 | | x-18+3x=-14 | | 2X+18=-8 | | 11n=5n+12 | | 2+2=5x | | 800-6x=1000-10x | | -4f+1.1=3.1 | | -120f=-160f | | 14-0.4(p-15)=0.1(3p-15) | | 100=25+.25x | | 4y/5-4/1+y/10=7/2 | | X/28=-50+30 | | -7(6x-7)+4(1+4x)=27 |

Equations solver categories