2n(n-1)=11

Solution for 2n(n-1)=11 equation:

Simplifying
2n(n + -1) = 11

Reorder the terms:
2n(-1 + n) = 11
(-1 * 2n + n * 2n) = 11
(-2n + 2n2) = 11

Solving
-2n + 2n2 = 11

Solving for variable 'n'.

Reorder the terms:
-11 + -2n + 2n2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -2n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-5.5 + -1n + n2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -1n + 5.5 + n2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -1n + n2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -1n + n2 = 0 + 5.5
-1n + n2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-1n + n2 = 5.5

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = 5.5 + 0.25

Reorder the terms:
0.25 + -1n + n2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
0.25 + -1n + n2 = 5.75

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(n + -0.5) equal to 2.397915762 and -2.397915762.

Subproblem 1
n + -0.5 = 2.397915762

Simplifying
n + -0.5 = 2.397915762

Reorder the terms:
-0.5 + n = 2.397915762

Solving
-0.5 + n = 2.397915762

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = 2.397915762 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = 2.397915762 + 0.5
n = 2.397915762 + 0.5

Combine like terms: 2.397915762 + 0.5 = 2.897915762
n = 2.897915762

Simplifying
n = 2.897915762

Subproblem 2
n + -0.5 = -2.397915762

Simplifying
n + -0.5 = -2.397915762

Reorder the terms:
-0.5 + n = -2.397915762

Solving
-0.5 + n = -2.397915762

Solving for variable 'n'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + n = -2.397915762 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + n = -2.397915762 + 0.5
n = -2.397915762 + 0.5

Combine like terms: -2.397915762 + 0.5 = -1.897915762
n = -1.897915762

Simplifying
n = -1.897915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.897915762, -1.897915762}