18x^2+16x-9=0

Solution for 18x^2+16x-9=0 equation:

Simplifying
18x2 + 16x + -9 = 0

Reorder the terms:
-9 + 16x + 18x2 = 0

Solving
-9 + 16x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
-0.5 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.8888888889x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.8888888889x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.8888888889x + x2 = 0 + 0.5
0.8888888889x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.8888888889x + x2 = 0.5

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 = 0.5 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 0.5 + 0.1975308642

Combine like terms: 0.5 + 0.1975308642 = 0.6975308642
0.1975308642 + 0.8888888889x + x2 = 0.6975308642

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 0.6975308642

Calculate the square root of the right side: 0.835183132

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 0.835183132 and -0.835183132.

Subproblem 1
x + 0.4444444445 = 0.835183132

Simplifying
x + 0.4444444445 = 0.835183132

Reorder the terms:
0.4444444445 + x = 0.835183132

Solving
0.4444444445 + x = 0.835183132

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 = 0.835183132 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = 0.835183132 + -0.4444444445
x = 0.835183132 + -0.4444444445

Combine like terms: 0.835183132 + -0.4444444445 = 0.3907386875
x = 0.3907386875

Simplifying
x = 0.3907386875

Subproblem 2
x + 0.4444444445 = -0.835183132

Simplifying
x + 0.4444444445 = -0.835183132

Reorder the terms:
0.4444444445 + x = -0.835183132

Solving
0.4444444445 + x = -0.835183132

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 = -0.835183132 + -0.4444444445

Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000
0.0000000000 + x = -0.835183132 + -0.4444444445
x = -0.835183132 + -0.4444444445

Combine like terms: -0.835183132 + -0.4444444445 = -1.2796275765
x = -1.2796275765

Simplifying
x = -1.2796275765

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3907386875, -1.2796275765}