2x^2+18x+1=0

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

Simplifying
2x2 + 18x + 1 = 0

Reorder the terms:
1 + 18x + 2x2 = 0

Solving
1 + 18x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
0.5 + 9x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 9x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 9x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 9x + x2 = 0 + -0.5
9x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
9x + x2 = -0.5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -0.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -0.5 + 20.25

Combine like terms: -0.5 + 20.25 = 19.75
20.25 + 9x + x2 = 19.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 19.75

Calculate the square root of the right side: 4.444097209

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.444097209 and -4.444097209.

Subproblem 1
x + 4.5 = 4.444097209

Simplifying
x + 4.5 = 4.444097209

Reorder the terms:
4.5 + x = 4.444097209

Solving
4.5 + x = 4.444097209

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.444097209 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.444097209 + -4.5
x = 4.444097209 + -4.5

Combine like terms: 4.444097209 + -4.5 = -0.055902791
x = -0.055902791

Simplifying
x = -0.055902791

Subproblem 2
x + 4.5 = -4.444097209

Simplifying
x + 4.5 = -4.444097209

Reorder the terms:
4.5 + x = -4.444097209

Solving
4.5 + x = -4.444097209

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.444097209 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.444097209 + -4.5
x = -4.444097209 + -4.5

Combine like terms: -4.444097209 + -4.5 = -8.944097209
x = -8.944097209

Simplifying
x = -8.944097209

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.055902791, -8.944097209}