0=18x^2-16x-4

Solution for 0=18x^2-16x-4 equation:

Simplifying
0 = 18x2 + -16x + -4

Reorder the terms:
0 = -4 + -16x + 18x2

Solving
0 = -4 + -16x + 18x2

Solving for variable 'x'.

Combine like terms: 0 + 4 = 4
4 + 16x + -18x2 = -4 + -16x + 18x2 + 4 + 16x + -18x2

Reorder the terms:
4 + 16x + -18x2 = -4 + 4 + -16x + 16x + 18x2 + -18x2

Combine like terms: -4 + 4 = 0
4 + 16x + -18x2 = 0 + -16x + 16x + 18x2 + -18x2
4 + 16x + -18x2 = -16x + 16x + 18x2 + -18x2

Combine like terms: -16x + 16x = 0
4 + 16x + -18x2 = 0 + 18x2 + -18x2
4 + 16x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
4 + 16x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 8x + -9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 8x + -9x2)' equal to zero and attempt to solve:

Simplifying
2 + 8x + -9x2 = 0

Solving
2 + 8x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.2222222222 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.8888888889x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.8888888889x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.8888888889x + x2 = 0 + 0.2222222222
-0.8888888889x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.8888888889x + x2 = 0.2222222222

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 0.2222222222 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 0.2222222222 + 0.1975308642

Combine like terms: 0.2222222222 + 0.1975308642 = 0.4197530864
0.1975308642 + -0.8888888889x + x2 = 0.4197530864

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 0.4197530864

Calculate the square root of the right side: 0.647883544

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 0.647883544 and -0.647883544.

Subproblem 1
x + -0.4444444445 = 0.647883544

Simplifying
x + -0.4444444445 = 0.647883544

Reorder the terms:
-0.4444444445 + x = 0.647883544

Solving
-0.4444444445 + x = 0.647883544

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = 0.647883544 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = 0.647883544 + 0.4444444445
x = 0.647883544 + 0.4444444445

Combine like terms: 0.647883544 + 0.4444444445 = 1.0923279885
x = 1.0923279885

Simplifying
x = 1.0923279885

Subproblem 2
x + -0.4444444445 = -0.647883544

Simplifying
x + -0.4444444445 = -0.647883544

Reorder the terms:
-0.4444444445 + x = -0.647883544

Solving
-0.4444444445 + x = -0.647883544

Solving for variable 'x'.

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

Add '0.4444444445' to each side of the equation.
-0.4444444445 + 0.4444444445 + x = -0.647883544 + 0.4444444445

Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000
0.0000000000 + x = -0.647883544 + 0.4444444445
x = -0.647883544 + 0.4444444445

Combine like terms: -0.647883544 + 0.4444444445 = -0.2034390995
x = -0.2034390995

Simplifying
x = -0.2034390995

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0923279885, -0.2034390995}
Solution
x = {1.0923279885, -0.2034390995}