n^2-2n-62=0

Solution for n^2-2n-62=0 equation:

Simplifying
n2 + -2n + -62 = 0

Reorder the terms:
-62 + -2n + n2 = 0

Solving
-62 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + -2n + 62 + n2 = 0 + 62

Reorder the terms:
-62 + 62 + -2n + n2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + -2n + n2 = 0 + 62
-2n + n2 = 0 + 62

Combine like terms: 0 + 62 = 62
-2n + n2 = 62

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 = 62 + 1

Reorder the terms:
1 + -2n + n2 = 62 + 1

Combine like terms: 62 + 1 = 63
1 + -2n + n2 = 63

Factor a perfect square on the left side:
(n + -1)(n + -1) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(n + -1) equal to 7.937253933 and -7.937253933.

Subproblem 1
n + -1 = 7.937253933

Simplifying
n + -1 = 7.937253933

Reorder the terms:
-1 + n = 7.937253933

Solving
-1 + n = 7.937253933

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 = 7.937253933 + 1

Combine like terms: -1 + 1 = 0
0 + n = 7.937253933 + 1
n = 7.937253933 + 1

Combine like terms: 7.937253933 + 1 = 8.937253933
n = 8.937253933

Simplifying
n = 8.937253933

Subproblem 2
n + -1 = -7.937253933

Simplifying
n + -1 = -7.937253933

Reorder the terms:
-1 + n = -7.937253933

Solving
-1 + n = -7.937253933

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 = -7.937253933 + 1

Combine like terms: -1 + 1 = 0
0 + n = -7.937253933 + 1
n = -7.937253933 + 1

Combine like terms: -7.937253933 + 1 = -6.937253933
n = -6.937253933

Simplifying
n = -6.937253933

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {8.937253933, -6.937253933}