n^2-2n-33=0

Solution for n^2-2n-33=0 equation:

Simplifying
n2 + -2n + -33 = 0

Reorder the terms:
-33 + -2n + n2 = 0

Solving
-33 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -2n + 33 + n2 = 0 + 33

Reorder the terms:
-33 + 33 + -2n + n2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -2n + n2 = 0 + 33
-2n + n2 = 0 + 33

Combine like terms: 0 + 33 = 33
-2n + n2 = 33

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 = 33 + 1

Reorder the terms:
1 + -2n + n2 = 33 + 1

Combine like terms: 33 + 1 = 34
1 + -2n + n2 = 34

Factor a perfect square on the left side:
(n + -1)(n + -1) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(n + -1) equal to 5.830951895 and -5.830951895.

Subproblem 1
n + -1 = 5.830951895

Simplifying
n + -1 = 5.830951895

Reorder the terms:
-1 + n = 5.830951895

Solving
-1 + n = 5.830951895

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 = 5.830951895 + 1

Combine like terms: -1 + 1 = 0
0 + n = 5.830951895 + 1
n = 5.830951895 + 1

Combine like terms: 5.830951895 + 1 = 6.830951895
n = 6.830951895

Simplifying
n = 6.830951895

Subproblem 2
n + -1 = -5.830951895

Simplifying
n + -1 = -5.830951895

Reorder the terms:
-1 + n = -5.830951895

Solving
-1 + n = -5.830951895

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 = -5.830951895 + 1

Combine like terms: -1 + 1 = 0
0 + n = -5.830951895 + 1
n = -5.830951895 + 1

Combine like terms: -5.830951895 + 1 = -4.830951895
n = -4.830951895

Simplifying
n = -4.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.830951895, -4.830951895}