n^2-8n+11=0

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Solution for n^2-8n+11=0 equation: 


Simplifying
n2 + -8n + 11 = 0

Reorder the terms:
11 + -8n + n2 = 0

Solving
11 + -8n + 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 + -8n + -11 + n2 = 0 + -11

Reorder the terms:
11 + -11 + -8n + n2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -8n + n2 = 0 + -11
-8n + n2 = 0 + -11

Combine like terms: 0 + -11 = -11
-8n + n2 = -11

The n term is -8n.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8n + 16 + n2 = -11 + 16

Reorder the terms:
16 + -8n + n2 = -11 + 16

Combine like terms: -11 + 16 = 5
16 + -8n + n2 = 5

Factor a perfect square on the left side:
(n + -4)(n + -4) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(n + -4) equal to 2.236067978 and -2.236067978.


Subproblem 1
n + -4 = 2.236067978

Simplifying
n + -4 = 2.236067978

Reorder the terms:
-4 + n = 2.236067978

Solving
-4 + n = 2.236067978

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = 2.236067978 + 4

Combine like terms: -4 + 4 = 0
0 + n = 2.236067978 + 4
n = 2.236067978 + 4

Combine like terms: 2.236067978 + 4 = 6.236067978
n = 6.236067978

Simplifying
n = 6.236067978


Subproblem 2
n + -4 = -2.236067978

Simplifying
n + -4 = -2.236067978

Reorder the terms:
-4 + n = -2.236067978

Solving
-4 + n = -2.236067978

Solving for variable 'n'.

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

Add '4' to each side of the equation.
-4 + 4 + n = -2.236067978 + 4

Combine like terms: -4 + 4 = 0
0 + n = -2.236067978 + 4
n = -2.236067978 + 4

Combine like terms: -2.236067978 + 4 = 1.763932022
n = 1.763932022

Simplifying
n = 1.763932022


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.236067978, 1.763932022}

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