-n^2+2n+17=0

Solution for -n^2+2n+17=0 equation:

Simplifying
-1n2 + 2n + 17 = 0

Reorder the terms:
17 + 2n + -1n2 = 0

Solving
17 + 2n + -1n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + -2n + n2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -2n + 17 + n2 = 0 + 17

Reorder the terms:
-17 + 17 + -2n + n2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2n + n2 = 0 + 17
-2n + n2 = 0 + 17

Combine like terms: 0 + 17 = 17
-2n + n2 = 17

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 = 17 + 1

Reorder the terms:
1 + -2n + n2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + -2n + n2 = 18

Factor a perfect square on the left side:
(n + -1)(n + -1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(n + -1) equal to 4.242640687 and -4.242640687.

Subproblem 1
n + -1 = 4.242640687

Simplifying
n + -1 = 4.242640687

Reorder the terms:
-1 + n = 4.242640687

Solving
-1 + n = 4.242640687

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 = 4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + n = 4.242640687 + 1
n = 4.242640687 + 1

Combine like terms: 4.242640687 + 1 = 5.242640687
n = 5.242640687

Simplifying
n = 5.242640687

Subproblem 2
n + -1 = -4.242640687

Simplifying
n + -1 = -4.242640687

Reorder the terms:
-1 + n = -4.242640687

Solving
-1 + n = -4.242640687

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 = -4.242640687 + 1

Combine like terms: -1 + 1 = 0
0 + n = -4.242640687 + 1
n = -4.242640687 + 1

Combine like terms: -4.242640687 + 1 = -3.242640687
n = -3.242640687

Simplifying
n = -3.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.242640687, -3.242640687}