n^2+6n-37=0

Solution for n^2+6n-37=0 equation:

Simplifying
n2 + 6n + -37 = 0

Reorder the terms:
-37 + 6n + n2 = 0

Solving
-37 + 6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 6n + 37 + n2 = 0 + 37

Reorder the terms:
-37 + 37 + 6n + n2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 6n + n2 = 0 + 37
6n + n2 = 0 + 37

Combine like terms: 0 + 37 = 37
6n + n2 = 37

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 = 37 + 9

Reorder the terms:
9 + 6n + n2 = 37 + 9

Combine like terms: 37 + 9 = 46
9 + 6n + n2 = 46

Factor a perfect square on the left side:
(n + 3)(n + 3) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(n + 3) equal to 6.782329983 and -6.782329983.

Subproblem 1
n + 3 = 6.782329983

Simplifying
n + 3 = 6.782329983

Reorder the terms:
3 + n = 6.782329983

Solving
3 + n = 6.782329983

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 = 6.782329983 + -3

Combine like terms: 3 + -3 = 0
0 + n = 6.782329983 + -3
n = 6.782329983 + -3

Combine like terms: 6.782329983 + -3 = 3.782329983
n = 3.782329983

Simplifying
n = 3.782329983

Subproblem 2
n + 3 = -6.782329983

Simplifying
n + 3 = -6.782329983

Reorder the terms:
3 + n = -6.782329983

Solving
3 + n = -6.782329983

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 = -6.782329983 + -3

Combine like terms: 3 + -3 = 0
0 + n = -6.782329983 + -3
n = -6.782329983 + -3

Combine like terms: -6.782329983 + -3 = -9.782329983
n = -9.782329983

Simplifying
n = -9.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.782329983, -9.782329983}