n^2-10n-16=0

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Solution for n^2-10n-16=0 equation: 


Simplifying
n2 + -10n + -16 = 0

Reorder the terms:
-16 + -10n + n2 = 0

Solving
-16 + -10n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -10n + 16 + n2 = 0 + 16

Reorder the terms:
-16 + 16 + -10n + n2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -10n + n2 = 0 + 16
-10n + n2 = 0 + 16

Combine like terms: 0 + 16 = 16
-10n + n2 = 16

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 = 16 + 25

Reorder the terms:
25 + -10n + n2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + -10n + n2 = 41

Factor a perfect square on the left side:
(n + -5)(n + -5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(n + -5) equal to 6.403124237 and -6.403124237.


Subproblem 1
n + -5 = 6.403124237

Simplifying
n + -5 = 6.403124237

Reorder the terms:
-5 + n = 6.403124237

Solving
-5 + n = 6.403124237

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 = 6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + n = 6.403124237 + 5
n = 6.403124237 + 5

Combine like terms: 6.403124237 + 5 = 11.403124237
n = 11.403124237

Simplifying
n = 11.403124237


Subproblem 2
n + -5 = -6.403124237

Simplifying
n + -5 = -6.403124237

Reorder the terms:
-5 + n = -6.403124237

Solving
-5 + n = -6.403124237

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 = -6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + n = -6.403124237 + 5
n = -6.403124237 + 5

Combine like terms: -6.403124237 + 5 = -1.403124237
n = -1.403124237

Simplifying
n = -1.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {11.403124237, -1.403124237}

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