n^2+2n-11=0

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

Simplifying
n2 + 2n + -11 = 0

Reorder the terms:
-11 + 2n + n2 = 0

Solving
-11 + 2n + 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 + 2n + 11 + n2 = 0 + 11

Reorder the terms:
-11 + 11 + 2n + n2 = 0 + 11

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

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

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 = 11 + 1

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

Combine like terms: 11 + 1 = 12
1 + 2n + n2 = 12

Factor a perfect square on the left side:
(n + 1)(n + 1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(n + 1) equal to 3.464101615 and -3.464101615.

Subproblem 1
n + 1 = 3.464101615

Simplifying
n + 1 = 3.464101615

Reorder the terms:
1 + n = 3.464101615

Solving
1 + n = 3.464101615

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 = 3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + n = 3.464101615 + -1
n = 3.464101615 + -1

Combine like terms: 3.464101615 + -1 = 2.464101615
n = 2.464101615

Simplifying
n = 2.464101615

Subproblem 2
n + 1 = -3.464101615

Simplifying
n + 1 = -3.464101615

Reorder the terms:
1 + n = -3.464101615

Solving
1 + n = -3.464101615

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 = -3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + n = -3.464101615 + -1
n = -3.464101615 + -1

Combine like terms: -3.464101615 + -1 = -4.464101615
n = -4.464101615

Simplifying
n = -4.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.464101615, -4.464101615}