-18x^2+36x-2=0

Solution for -18x^2+36x-2=0 equation:

Simplifying
-18x2 + 36x + -2 = 0

Reorder the terms:
-2 + 36x + -18x2 = 0

Solving
-2 + 36x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 18x + -9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 18x + -9x2)' equal to zero and attempt to solve:

Simplifying
-1 + 18x + -9x2 = 0

Solving
-1 + 18x + -9x2 = 0

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 = 1.942809042
x = 1.942809042

Simplifying
x = 1.942809042

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 = 0.057190958
x = 0.057190958

Simplifying
x = 0.057190958

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