(9x)(9x)+(54x)=18

Solution for (9x)(9x)+(54x)=18 equation:

Simplifying
(9x)(9x) + (54x) = 18

Remove parenthesis around (9x)
9x(9x) + (54x) = 18

Remove parenthesis around (9x)
9x * 9x + (54x) = 18

Reorder the terms for easier multiplication:
9 * 9x * x + (54x) = 18

Multiply 9 * 9
81x * x + (54x) = 18

Multiply x * x
81x2 + (54x) = 18

Reorder the terms:
(54x) + 81x2 = 18

Solving
(54x) + 81x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + (54x) + 81x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + (54x) + 81x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + (6x) + 9x2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-2 + (6x) + 9x2)' equal to zero and attempt to solve:

Simplifying
-2 + (6x) + 9x2 = 0

Solving
-2 + (6x) + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + (0.6666666667x) + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + (0.6666666667x) + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + (0.6666666667x) + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + (0.6666666667x) + x2 = 0 + 0.2222222222
(0.6666666667x) + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
(0.6666666667x) + x2 = 0.2222222222

The x term is (0.6666666667x).  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
(0.6666666667x) + 0.1111111112 + x2 = 0.2222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + (0.6666666667x) + x2 = 0.2222222222 + 0.1111111112

Combine like terms: 0.2222222222 + 0.1111111112 = 0.3333333334
0.1111111112 + (0.6666666667x) + x2 = 0.3333333334

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.3333333334

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.577350269 and -0.577350269.

Subproblem 1
x + 0.3333333334 = 0.577350269

Simplifying
x + 0.3333333334 = 0.577350269

Reorder the terms:
0.3333333334 + x = 0.577350269

Solving
0.3333333334 + x = 0.577350269

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 0.577350269 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 0.577350269 + -0.3333333334
x = 0.577350269 + -0.3333333334

Combine like terms: 0.577350269 + -0.3333333334 = 0.2440169356
x = 0.2440169356

Simplifying
x = 0.2440169356

Subproblem 2
x + 0.3333333334 = -0.577350269

Simplifying
x + 0.3333333334 = -0.577350269

Reorder the terms:
0.3333333334 + x = -0.577350269

Solving
0.3333333334 + x = -0.577350269

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -0.577350269 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -0.577350269 + -0.3333333334
x = -0.577350269 + -0.3333333334

Combine like terms: -0.577350269 + -0.3333333334 = -0.9106836024
x = -0.9106836024

Simplifying
x = -0.9106836024

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2440169356, -0.9106836024}
Solution
x = {0.2440169356, -0.9106836024}