n^2-2n-73=0

Solution for n^2-2n-73=0 equation:

Simplifying
n2 + -2n + -73 = 0

Reorder the terms:
-73 + -2n + n2 = 0

Solving
-73 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '73' to each side of the equation.
-73 + -2n + 73 + n2 = 0 + 73

Reorder the terms:
-73 + 73 + -2n + n2 = 0 + 73

Combine like terms: -73 + 73 = 0
0 + -2n + n2 = 0 + 73
-2n + n2 = 0 + 73

Combine like terms: 0 + 73 = 73
-2n + n2 = 73

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 = 73 + 1

Reorder the terms:
1 + -2n + n2 = 73 + 1

Combine like terms: 73 + 1 = 74
1 + -2n + n2 = 74

Factor a perfect square on the left side:
(n + -1)(n + -1) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(n + -1) equal to 8.602325267 and -8.602325267.

Subproblem 1
n + -1 = 8.602325267

Simplifying
n + -1 = 8.602325267

Reorder the terms:
-1 + n = 8.602325267

Solving
-1 + n = 8.602325267

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 = 8.602325267 + 1

Combine like terms: -1 + 1 = 0
0 + n = 8.602325267 + 1
n = 8.602325267 + 1

Combine like terms: 8.602325267 + 1 = 9.602325267
n = 9.602325267

Simplifying
n = 9.602325267

Subproblem 2
n + -1 = -8.602325267

Simplifying
n + -1 = -8.602325267

Reorder the terms:
-1 + n = -8.602325267

Solving
-1 + n = -8.602325267

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 = -8.602325267 + 1

Combine like terms: -1 + 1 = 0
0 + n = -8.602325267 + 1
n = -8.602325267 + 1

Combine like terms: -8.602325267 + 1 = -7.602325267
n = -7.602325267

Simplifying
n = -7.602325267

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.602325267, -7.602325267}