1000=0.5n(9.6+(n-1)2.8)

Solution for 1000=0.5n(9.6+(n-1)2.8) equation:

Simplifying
1000 = 0.5n(9.6 + (n + -1) * 2.8)

Reorder the terms:
1000 = 0.5n(9.6 + (-1 + n) * 2.8)

Reorder the terms for easier multiplication:
1000 = 0.5n(9.6 + 2.8(-1 + n))
1000 = 0.5n(9.6 + (-1 * 2.8 + n * 2.8))
1000 = 0.5n(9.6 + (-2.8 + 2.8n))

Combine like terms: 9.6 + -2.8 = 6.8
1000 = 0.5n(6.8 + 2.8n)
1000 = (6.8 * 0.5n + 2.8n * 0.5n)
1000 = (3.4n + 1.4n2)

Solving
1000 = 3.4n + 1.4n2

Solving for variable 'n'.

Reorder the terms:
1000 + -3.4n + -1.4n2 = 3.4n + -3.4n + 1.4n2 + -1.4n2

Combine like terms: 3.4n + -3.4n = 0.0
1000 + -3.4n + -1.4n2 = 0.0 + 1.4n2 + -1.4n2
1000 + -3.4n + -1.4n2 = 1.4n2 + -1.4n2

Combine like terms: 1.4n2 + -1.4n2 = 0.0
1000 + -3.4n + -1.4n2 = 0.0

Begin completing the square.  Divide all terms by
-1.4 the coefficient of the squared term: 

Divide each side by '-1.4'.
-714.2857143 + 2.428571429n + n2 = 0

Move the constant term to the right:

Add '714.2857143' to each side of the equation.
-714.2857143 + 2.428571429n + 714.2857143 + n2 = 0 + 714.2857143

Reorder the terms:
-714.2857143 + 714.2857143 + 2.428571429n + n2 = 0 + 714.2857143

Combine like terms: -714.2857143 + 714.2857143 = 0.0000000
0.0000000 + 2.428571429n + n2 = 0 + 714.2857143
2.428571429n + n2 = 0 + 714.2857143

Combine like terms: 0 + 714.2857143 = 714.2857143
2.428571429n + n2 = 714.2857143

The n term is 2.428571429n.  Take half its coefficient (1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
2.428571429n + 1.474489798 + n2 = 714.2857143 + 1.474489798

Reorder the terms:
1.474489798 + 2.428571429n + n2 = 714.2857143 + 1.474489798

Combine like terms: 714.2857143 + 1.474489798 = 715.760204098
1.474489798 + 2.428571429n + n2 = 715.760204098

Factor a perfect square on the left side:
(n + 1.214285715)(n + 1.214285715) = 715.760204098

Calculate the square root of the right side: 26.753695148

Break this problem into two subproblems by setting 
(n + 1.214285715) equal to 26.753695148 and -26.753695148.

Subproblem 1
n + 1.214285715 = 26.753695148

Simplifying
n + 1.214285715 = 26.753695148

Reorder the terms:
1.214285715 + n = 26.753695148

Solving
1.214285715 + n = 26.753695148

Solving for variable 'n'.

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

Add '-1.214285715' to each side of the equation.
1.214285715 + -1.214285715 + n = 26.753695148 + -1.214285715

Combine like terms: 1.214285715 + -1.214285715 = 0.000000000
0.000000000 + n = 26.753695148 + -1.214285715
n = 26.753695148 + -1.214285715

Combine like terms: 26.753695148 + -1.214285715 = 25.539409433
n = 25.539409433

Simplifying
n = 25.539409433

Subproblem 2
n + 1.214285715 = -26.753695148

Simplifying
n + 1.214285715 = -26.753695148

Reorder the terms:
1.214285715 + n = -26.753695148

Solving
1.214285715 + n = -26.753695148

Solving for variable 'n'.

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

Add '-1.214285715' to each side of the equation.
1.214285715 + -1.214285715 + n = -26.753695148 + -1.214285715

Combine like terms: 1.214285715 + -1.214285715 = 0.000000000
0.000000000 + n = -26.753695148 + -1.214285715
n = -26.753695148 + -1.214285715

Combine like terms: -26.753695148 + -1.214285715 = -27.967980863
n = -27.967980863

Simplifying
n = -27.967980863

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {25.539409433, -27.967980863}