x^2-18x-2=0

Solution for x^2-18x-2=0 equation:

Simplifying
x2 + -18x + -2 = 0

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

Solving
-2 + -18x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -18x + 2 + x2 = 0 + 2

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

Combine like terms: -2 + 2 = 0
0 + -18x + x2 = 0 + 2
-18x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-18x + x2 = 2

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 = 2 + 81

Reorder the terms:
81 + -18x + x2 = 2 + 81

Combine like terms: 2 + 81 = 83
81 + -18x + x2 = 83

Factor a perfect square on the left side:
(x + -9)(x + -9) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(x + -9) equal to 9.110433579 and -9.110433579.

Subproblem 1
x + -9 = 9.110433579

Simplifying
x + -9 = 9.110433579

Reorder the terms:
-9 + x = 9.110433579

Solving
-9 + x = 9.110433579

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 = 9.110433579 + 9

Combine like terms: -9 + 9 = 0
0 + x = 9.110433579 + 9
x = 9.110433579 + 9

Combine like terms: 9.110433579 + 9 = 18.110433579
x = 18.110433579

Simplifying
x = 18.110433579

Subproblem 2
x + -9 = -9.110433579

Simplifying
x + -9 = -9.110433579

Reorder the terms:
-9 + x = -9.110433579

Solving
-9 + x = -9.110433579

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 = -9.110433579 + 9

Combine like terms: -9 + 9 = 0
0 + x = -9.110433579 + 9
x = -9.110433579 + 9

Combine like terms: -9.110433579 + 9 = -0.110433579
x = -0.110433579

Simplifying
x = -0.110433579

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.110433579, -0.110433579}