n^2-6n-5=0

Solution for n^2-6n-5=0 equation:

Simplifying
n2 + -6n + -5 = 0

Reorder the terms:
-5 + -6n + n2 = 0

Solving
-5 + -6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + -6n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6n + n2 = 0 + 5
-6n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-6n + n2 = 5

The n term is -6n.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6n + 9 + n2 = 5 + 9

Reorder the terms:
9 + -6n + n2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + -6n + n2 = 14

Factor a perfect square on the left side:
(n + -3)(n + -3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(n + -3) equal to 3.741657387 and -3.741657387.

Subproblem 1
n + -3 = 3.741657387

Simplifying
n + -3 = 3.741657387

Reorder the terms:
-3 + n = 3.741657387

Solving
-3 + n = 3.741657387

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + n = 3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + n = 3.741657387 + 3
n = 3.741657387 + 3

Combine like terms: 3.741657387 + 3 = 6.741657387
n = 6.741657387

Simplifying
n = 6.741657387

Subproblem 2
n + -3 = -3.741657387

Simplifying
n + -3 = -3.741657387

Reorder the terms:
-3 + n = -3.741657387

Solving
-3 + n = -3.741657387

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + n = -3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + n = -3.741657387 + 3
n = -3.741657387 + 3

Combine like terms: -3.741657387 + 3 = -0.741657387
n = -0.741657387

Simplifying
n = -0.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.741657387, -0.741657387}