x^2-2x-11=0

Solution for x^2-2x-11=0 equation:

Simplifying
x2 + -2x + -11 = 0

Reorder the terms:
-11 + -2x + x2 = 0

Solving
-11 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -2x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2x + x2 = 0 + 11
-2x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2x + x2 = 11

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

Add '1' to each side of the equation.
-2x + 1 + x2 = 11 + 1

Reorder the terms:
1 + -2x + x2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + -2x + x2 = 12

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

Calculate the square root of the right side: 3.464101615

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

Subproblem 1
x + -1 = 3.464101615

Simplifying
x + -1 = 3.464101615

Reorder the terms:
-1 + x = 3.464101615

Solving
-1 + x = 3.464101615

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.464101615 + 1

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

Combine like terms: 3.464101615 + 1 = 4.464101615
x = 4.464101615

Simplifying
x = 4.464101615

Subproblem 2
x + -1 = -3.464101615

Simplifying
x + -1 = -3.464101615

Reorder the terms:
-1 + x = -3.464101615

Solving
-1 + x = -3.464101615

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.464101615 + 1

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

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

Simplifying
x = -2.464101615

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