n^2+2n+1=11

Solution for n^2+2n+1=11 equation:

Simplifying
n2 + 2n + 1 = 11

Reorder the terms:
1 + 2n + n2 = 11

Solving
1 + 2n + n2 = 11

Solving for variable 'n'.

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

Combine like terms: 1 + -11 = -10
-10 + 2n + n2 = 11 + -11

Combine like terms: 11 + -11 = 0
-10 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2n + 10 + n2 = 0 + 10

Reorder the terms:
-10 + 10 + 2n + n2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2n + n2 = 0 + 10
2n + n2 = 0 + 10

Combine like terms: 0 + 10 = 10
2n + n2 = 10

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 10 + 1

Reorder the terms:
1 + 2n + n2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2n + n2 = 11

Factor a perfect square on the left side:
(n + 1)(n + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(n + 1) equal to 3.31662479 and -3.31662479.

Subproblem 1
n + 1 = 3.31662479

Simplifying
n + 1 = 3.31662479

Reorder the terms:
1 + n = 3.31662479

Solving
1 + n = 3.31662479

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + n = 3.31662479 + -1
n = 3.31662479 + -1

Combine like terms: 3.31662479 + -1 = 2.31662479
n = 2.31662479

Simplifying
n = 2.31662479

Subproblem 2
n + 1 = -3.31662479

Simplifying
n + 1 = -3.31662479

Reorder the terms:
1 + n = -3.31662479

Solving
1 + n = -3.31662479

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + n = -3.31662479 + -1
n = -3.31662479 + -1

Combine like terms: -3.31662479 + -1 = -4.31662479
n = -4.31662479

Simplifying
n = -4.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.31662479, -4.31662479}