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 = 82
81 + 18x + x2 = 82

Factor a perfect square on the left side:
(x + 9)(x + 9) = 82

Calculate the square root of the right side: 9.055385138

Break this problem into two subproblems by setting 
(x + 9) equal to 9.055385138 and -9.055385138.

Subproblem 1
x + 9 = 9.055385138

Simplifying
x + 9 = 9.055385138

Reorder the terms:
9 + x = 9.055385138

Solving
9 + x = 9.055385138

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 = 9.055385138 + -9

Combine like terms: 9 + -9 = 0
0 + x = 9.055385138 + -9
x = 9.055385138 + -9

Combine like terms: 9.055385138 + -9 = 0.055385138
x = 0.055385138

Simplifying
x = 0.055385138

Subproblem 2
x + 9 = -9.055385138

Simplifying
x + 9 = -9.055385138

Reorder the terms:
9 + x = -9.055385138

Solving
9 + x = -9.055385138

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 = -9.055385138 + -9

Combine like terms: 9 + -9 = 0
0 + x = -9.055385138 + -9
x = -9.055385138 + -9

Combine like terms: -9.055385138 + -9 = -18.055385138
x = -18.055385138

Simplifying
x = -18.055385138

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.055385138, -18.055385138}