n^2-2n-59=0

Solution for n^2-2n-59=0 equation:

Simplifying
n2 + -2n + -59 = 0

Reorder the terms:
-59 + -2n + n2 = 0

Solving
-59 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '59' to each side of the equation.
-59 + -2n + 59 + n2 = 0 + 59

Reorder the terms:
-59 + 59 + -2n + n2 = 0 + 59

Combine like terms: -59 + 59 = 0
0 + -2n + n2 = 0 + 59
-2n + n2 = 0 + 59

Combine like terms: 0 + 59 = 59
-2n + n2 = 59

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 = 59 + 1

Reorder the terms:
1 + -2n + n2 = 59 + 1

Combine like terms: 59 + 1 = 60
1 + -2n + n2 = 60

Factor a perfect square on the left side:
(n + -1)(n + -1) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(n + -1) equal to 7.745966692 and -7.745966692.

Subproblem 1
n + -1 = 7.745966692

Simplifying
n + -1 = 7.745966692

Reorder the terms:
-1 + n = 7.745966692

Solving
-1 + n = 7.745966692

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 = 7.745966692 + 1

Combine like terms: -1 + 1 = 0
0 + n = 7.745966692 + 1
n = 7.745966692 + 1

Combine like terms: 7.745966692 + 1 = 8.745966692
n = 8.745966692

Simplifying
n = 8.745966692

Subproblem 2
n + -1 = -7.745966692

Simplifying
n + -1 = -7.745966692

Reorder the terms:
-1 + n = -7.745966692

Solving
-1 + n = -7.745966692

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 = -7.745966692 + 1

Combine like terms: -1 + 1 = 0
0 + n = -7.745966692 + 1
n = -7.745966692 + 1

Combine like terms: -7.745966692 + 1 = -6.745966692
n = -6.745966692

Simplifying
n = -6.745966692

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.745966692, -6.745966692}