n^2-16n-11=0

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Solution for n^2-16n-11=0 equation: 


Simplifying
n2 + -16n + -11 = 0

Reorder the terms:
-11 + -16n + n2 = 0

Solving
-11 + -16n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -16n + 11 + n2 = 0 + 11

Reorder the terms:
-11 + 11 + -16n + n2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -16n + n2 = 0 + 11
-16n + n2 = 0 + 11

Combine like terms: 0 + 11 = 11
-16n + n2 = 11

The n term is -16n.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16n + 64 + n2 = 11 + 64

Reorder the terms:
64 + -16n + n2 = 11 + 64

Combine like terms: 11 + 64 = 75
64 + -16n + n2 = 75

Factor a perfect square on the left side:
(n + -8)(n + -8) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(n + -8) equal to 8.660254038 and -8.660254038.


Subproblem 1
n + -8 = 8.660254038

Simplifying
n + -8 = 8.660254038

Reorder the terms:
-8 + n = 8.660254038

Solving
-8 + n = 8.660254038

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + n = 8.660254038 + 8

Combine like terms: -8 + 8 = 0
0 + n = 8.660254038 + 8
n = 8.660254038 + 8

Combine like terms: 8.660254038 + 8 = 16.660254038
n = 16.660254038

Simplifying
n = 16.660254038


Subproblem 2
n + -8 = -8.660254038

Simplifying
n + -8 = -8.660254038

Reorder the terms:
-8 + n = -8.660254038

Solving
-8 + n = -8.660254038

Solving for variable 'n'.

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

Add '8' to each side of the equation.
-8 + 8 + n = -8.660254038 + 8

Combine like terms: -8 + 8 = 0
0 + n = -8.660254038 + 8
n = -8.660254038 + 8

Combine like terms: -8.660254038 + 8 = -0.660254038
n = -0.660254038

Simplifying
n = -0.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {16.660254038, -0.660254038}

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