n^2-2n-78=0

Solution for n^2-2n-78=0 equation:

Simplifying
n2 + -2n + -78 = 0

Reorder the terms:
-78 + -2n + n2 = 0

Solving
-78 + -2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + -2n + 78 + n2 = 0 + 78

Reorder the terms:
-78 + 78 + -2n + n2 = 0 + 78

Combine like terms: -78 + 78 = 0
0 + -2n + n2 = 0 + 78
-2n + n2 = 0 + 78

Combine like terms: 0 + 78 = 78
-2n + n2 = 78

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 = 78 + 1

Reorder the terms:
1 + -2n + n2 = 78 + 1

Combine like terms: 78 + 1 = 79
1 + -2n + n2 = 79

Factor a perfect square on the left side:
(n + -1)(n + -1) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(n + -1) equal to 8.888194417 and -8.888194417.

Subproblem 1
n + -1 = 8.888194417

Simplifying
n + -1 = 8.888194417

Reorder the terms:
-1 + n = 8.888194417

Solving
-1 + n = 8.888194417

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 = 8.888194417 + 1

Combine like terms: -1 + 1 = 0
0 + n = 8.888194417 + 1
n = 8.888194417 + 1

Combine like terms: 8.888194417 + 1 = 9.888194417
n = 9.888194417

Simplifying
n = 9.888194417

Subproblem 2
n + -1 = -8.888194417

Simplifying
n + -1 = -8.888194417

Reorder the terms:
-1 + n = -8.888194417

Solving
-1 + n = -8.888194417

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 = -8.888194417 + 1

Combine like terms: -1 + 1 = 0
0 + n = -8.888194417 + 1
n = -8.888194417 + 1

Combine like terms: -8.888194417 + 1 = -7.888194417
n = -7.888194417

Simplifying
n = -7.888194417

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {9.888194417, -7.888194417}