n^2+10n-5=0

Solution for n^2+10n-5=0 equation:

Simplifying
n2 + 10n + -5 = 0

Reorder the terms:
-5 + 10n + n2 = 0

Solving
-5 + 10n + 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 + 10n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + 10n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 10n + n2 = 0 + 5
10n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
10n + n2 = 5

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 = 5 + 25

Reorder the terms:
25 + 10n + n2 = 5 + 25

Combine like terms: 5 + 25 = 30
25 + 10n + n2 = 30

Factor a perfect square on the left side:
(n + 5)(n + 5) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(n + 5) equal to 5.477225575 and -5.477225575.

Subproblem 1
n + 5 = 5.477225575

Simplifying
n + 5 = 5.477225575

Reorder the terms:
5 + n = 5.477225575

Solving
5 + n = 5.477225575

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 = 5.477225575 + -5

Combine like terms: 5 + -5 = 0
0 + n = 5.477225575 + -5
n = 5.477225575 + -5

Combine like terms: 5.477225575 + -5 = 0.477225575
n = 0.477225575

Simplifying
n = 0.477225575

Subproblem 2
n + 5 = -5.477225575

Simplifying
n + 5 = -5.477225575

Reorder the terms:
5 + n = -5.477225575

Solving
5 + n = -5.477225575

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 = -5.477225575 + -5

Combine like terms: 5 + -5 = 0
0 + n = -5.477225575 + -5
n = -5.477225575 + -5

Combine like terms: -5.477225575 + -5 = -10.477225575
n = -10.477225575

Simplifying
n = -10.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.477225575, -10.477225575}