11x^2+22x+1=0

Solution for 11x^2+22x+1=0 equation:

Simplifying
11x2 + 22x + 1 = 0

Reorder the terms:
1 + 22x + 11x2 = 0

Solving
1 + 22x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
0.09090909091 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.09090909091' to each side of the equation.
0.09090909091 + 2x + -0.09090909091 + x2 = 0 + -0.09090909091

Reorder the terms:
0.09090909091 + -0.09090909091 + 2x + x2 = 0 + -0.09090909091

Combine like terms: 0.09090909091 + -0.09090909091 = 0.00000000000
0.00000000000 + 2x + x2 = 0 + -0.09090909091
2x + x2 = 0 + -0.09090909091

Combine like terms: 0 + -0.09090909091 = -0.09090909091
2x + x2 = -0.09090909091

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 = -0.09090909091 + 1

Reorder the terms:
1 + 2x + x2 = -0.09090909091 + 1

Combine like terms: -0.09090909091 + 1 = 0.90909090909
1 + 2x + x2 = 0.90909090909

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.90909090909

Calculate the square root of the right side: 0.953462589

Break this problem into two subproblems by setting 
(x + 1) equal to 0.953462589 and -0.953462589.

Subproblem 1
x + 1 = 0.953462589

Simplifying
x + 1 = 0.953462589

Reorder the terms:
1 + x = 0.953462589

Solving
1 + x = 0.953462589

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 = 0.953462589 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.953462589 + -1
x = 0.953462589 + -1

Combine like terms: 0.953462589 + -1 = -0.046537411
x = -0.046537411

Simplifying
x = -0.046537411

Subproblem 2
x + 1 = -0.953462589

Simplifying
x + 1 = -0.953462589

Reorder the terms:
1 + x = -0.953462589

Solving
1 + x = -0.953462589

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 = -0.953462589 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.953462589 + -1
x = -0.953462589 + -1

Combine like terms: -0.953462589 + -1 = -1.953462589
x = -1.953462589

Simplifying
x = -1.953462589

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.046537411, -1.953462589}