n^2-2n-5003=0

Solution for n^2-2n-5003=0 equation:

Simplifying
n2 + -2n + -5003 = 0

Reorder the terms:
-5003 + -2n + n2 = 0

Solving
-5003 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '5003' to each side of the equation.
-5003 + -2n + 5003 + n2 = 0 + 5003

Reorder the terms:
-5003 + 5003 + -2n + n2 = 0 + 5003

Combine like terms: -5003 + 5003 = 0
0 + -2n + n2 = 0 + 5003
-2n + n2 = 0 + 5003

Combine like terms: 0 + 5003 = 5003
-2n + n2 = 5003

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 = 5003 + 1

Reorder the terms:
1 + -2n + n2 = 5003 + 1

Combine like terms: 5003 + 1 = 5004
1 + -2n + n2 = 5004

Factor a perfect square on the left side:
(n + -1)(n + -1) = 5004

Calculate the square root of the right side: 70.738956735

Break this problem into two subproblems by setting 
(n + -1) equal to 70.738956735 and -70.738956735.

Subproblem 1
n + -1 = 70.738956735

Simplifying
n + -1 = 70.738956735

Reorder the terms:
-1 + n = 70.738956735

Solving
-1 + n = 70.738956735

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 = 70.738956735 + 1

Combine like terms: -1 + 1 = 0
0 + n = 70.738956735 + 1
n = 70.738956735 + 1

Combine like terms: 70.738956735 + 1 = 71.738956735
n = 71.738956735

Simplifying
n = 71.738956735

Subproblem 2
n + -1 = -70.738956735

Simplifying
n + -1 = -70.738956735

Reorder the terms:
-1 + n = -70.738956735

Solving
-1 + n = -70.738956735

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 = -70.738956735 + 1

Combine like terms: -1 + 1 = 0
0 + n = -70.738956735 + 1
n = -70.738956735 + 1

Combine like terms: -70.738956735 + 1 = -69.738956735
n = -69.738956735

Simplifying
n = -69.738956735

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {71.738956735, -69.738956735}