9x^2+18x+1=0

Solution for 9x^2+18x+1=0 equation:

Simplifying
9x2 + 18x + 1 = 0

Reorder the terms:
1 + 18x + 9x2 = 0

Solving
1 + 18x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
0.1111111111 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + 2x + -0.1111111111 + x2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + 2x + x2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + -0.1111111111
2x + x2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
2x + x2 = -0.1111111111

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 = -0.1111111111 + 1

Reorder the terms:
1 + 2x + x2 = -0.1111111111 + 1

Combine like terms: -0.1111111111 + 1 = 0.8888888889
1 + 2x + x2 = 0.8888888889

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.8888888889

Calculate the square root of the right side: 0.942809042

Break this problem into two subproblems by setting 
(x + 1) equal to 0.942809042 and -0.942809042.

Subproblem 1
x + 1 = 0.942809042

Simplifying
x + 1 = 0.942809042

Reorder the terms:
1 + x = 0.942809042

Solving
1 + x = 0.942809042

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 = 0.942809042 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.942809042 + -1
x = 0.942809042 + -1

Combine like terms: 0.942809042 + -1 = -0.057190958
x = -0.057190958

Simplifying
x = -0.057190958

Subproblem 2
x + 1 = -0.942809042

Simplifying
x + 1 = -0.942809042

Reorder the terms:
1 + x = -0.942809042

Solving
1 + x = -0.942809042

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 = -0.942809042 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.942809042 + -1
x = -0.942809042 + -1

Combine like terms: -0.942809042 + -1 = -1.942809042
x = -1.942809042

Simplifying
x = -1.942809042

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.057190958, -1.942809042}