6+(9+x)=9x^2

Solution for 6+(9+x)=9x^2 equation:

Simplifying
6 + (9 + x) = 9x2

Remove parenthesis around (9 + x)
6 + 9 + x = 9x2

Combine like terms: 6 + 9 = 15
15 + x = 9x2

Solving
15 + x = 9x2

Solving for variable 'x'.

Combine like terms: 9x2 + -9x2 = 0
15 + x + -9x2 = 0

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

Divide each side by '-9'.
-1.666666667 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -0.1111111111x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -0.1111111111x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -0.1111111111x + x2 = 0 + 1.666666667
-0.1111111111x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-0.1111111111x + x2 = 1.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.1111111111x + 0.25 + x2 = 1.666666667 + 0.25

Reorder the terms:
0.25 + -0.1111111111x + x2 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + -0.1111111111x + x2 = 1.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.384437311 and -1.384437311.

Subproblem 1
x + 0.5 = 1.384437311

Simplifying
x + 0.5 = 1.384437311

Reorder the terms:
0.5 + x = 1.384437311

Solving
0.5 + x = 1.384437311

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.384437311 + -0.5
x = 1.384437311 + -0.5

Combine like terms: 1.384437311 + -0.5 = 0.884437311
x = 0.884437311

Simplifying
x = 0.884437311

Subproblem 2
x + 0.5 = -1.384437311

Simplifying
x + 0.5 = -1.384437311

Reorder the terms:
0.5 + x = -1.384437311

Solving
0.5 + x = -1.384437311

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.384437311 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.384437311 + -0.5
x = -1.384437311 + -0.5

Combine like terms: -1.384437311 + -0.5 = -1.884437311
x = -1.884437311

Simplifying
x = -1.884437311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.884437311, -1.884437311}