x^2+18x+1=0

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

Simplifying
x2 + 18x + 1 = 0

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

Solving
1 + 18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 18x + -1 + x2 = 0 + -1

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

Combine like terms: 1 + -1 = 0
0 + 18x + x2 = 0 + -1
18x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
18x + x2 = -1

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -1 + 81

Reorder the terms:
81 + 18x + x2 = -1 + 81

Combine like terms: -1 + 81 = 80
81 + 18x + x2 = 80

Factor a perfect square on the left side:
(x + 9)(x + 9) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + 9) equal to 8.94427191 and -8.94427191.

Subproblem 1
x + 9 = 8.94427191

Simplifying
x + 9 = 8.94427191

Reorder the terms:
9 + x = 8.94427191

Solving
9 + x = 8.94427191

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = 8.94427191 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.94427191 + -9
x = 8.94427191 + -9

Combine like terms: 8.94427191 + -9 = -0.05572809
x = -0.05572809

Simplifying
x = -0.05572809

Subproblem 2
x + 9 = -8.94427191

Simplifying
x + 9 = -8.94427191

Reorder the terms:
9 + x = -8.94427191

Solving
9 + x = -8.94427191

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + x = -8.94427191 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.94427191 + -9
x = -8.94427191 + -9

Combine like terms: -8.94427191 + -9 = -17.94427191
x = -17.94427191

Simplifying
x = -17.94427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.05572809, -17.94427191}