n^2+10n-6=0

Solution for n^2+10n-6=0 equation:

Simplifying
n2 + 10n + -6 = 0

Reorder the terms:
-6 + 10n + n2 = 0

Solving
-6 + 10n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 10n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + 10n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 10n + n2 = 0 + 6
10n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
10n + n2 = 6

The n term is 10n.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10n + 25 + n2 = 6 + 25

Reorder the terms:
25 + 10n + n2 = 6 + 25

Combine like terms: 6 + 25 = 31
25 + 10n + n2 = 31

Factor a perfect square on the left side:
(n + 5)(n + 5) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(n + 5) equal to 5.567764363 and -5.567764363.

Subproblem 1
n + 5 = 5.567764363

Simplifying
n + 5 = 5.567764363

Reorder the terms:
5 + n = 5.567764363

Solving
5 + n = 5.567764363

Solving for variable 'n'.

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

Add '-5' to each side of the equation.
5 + -5 + n = 5.567764363 + -5

Combine like terms: 5 + -5 = 0
0 + n = 5.567764363 + -5
n = 5.567764363 + -5

Combine like terms: 5.567764363 + -5 = 0.567764363
n = 0.567764363

Simplifying
n = 0.567764363

Subproblem 2
n + 5 = -5.567764363

Simplifying
n + 5 = -5.567764363

Reorder the terms:
5 + n = -5.567764363

Solving
5 + n = -5.567764363

Solving for variable 'n'.

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

Add '-5' to each side of the equation.
5 + -5 + n = -5.567764363 + -5

Combine like terms: 5 + -5 = 0
0 + n = -5.567764363 + -5
n = -5.567764363 + -5

Combine like terms: -5.567764363 + -5 = -10.567764363
n = -10.567764363

Simplifying
n = -10.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.567764363, -10.567764363}