n^2+6n-1=0

Solution for n^2+6n-1=0 equation:

Simplifying
n2 + 6n + -1 = 0

Reorder the terms:
-1 + 6n + n2 = 0

Solving
-1 + 6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 6n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 6n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 6n + n2 = 0 + 1
6n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
6n + n2 = 1

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 = 1 + 9

Reorder the terms:
9 + 6n + n2 = 1 + 9

Combine like terms: 1 + 9 = 10
9 + 6n + n2 = 10

Factor a perfect square on the left side:
(n + 3)(n + 3) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(n + 3) equal to 3.16227766 and -3.16227766.

Subproblem 1
n + 3 = 3.16227766

Simplifying
n + 3 = 3.16227766

Reorder the terms:
3 + n = 3.16227766

Solving
3 + n = 3.16227766

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 = 3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + n = 3.16227766 + -3
n = 3.16227766 + -3

Combine like terms: 3.16227766 + -3 = 0.16227766
n = 0.16227766

Simplifying
n = 0.16227766

Subproblem 2
n + 3 = -3.16227766

Simplifying
n + 3 = -3.16227766

Reorder the terms:
3 + n = -3.16227766

Solving
3 + n = -3.16227766

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 = -3.16227766 + -3

Combine like terms: 3 + -3 = 0
0 + n = -3.16227766 + -3
n = -3.16227766 + -3

Combine like terms: -3.16227766 + -3 = -6.16227766
n = -6.16227766

Simplifying
n = -6.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.16227766, -6.16227766}