9x(x+9)=135

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Solution for 9x(x+9)=135 equation: 


Simplifying
9x(x + 9) = 135

Reorder the terms:
9x(9 + x) = 135
(9 * 9x + x * 9x) = 135
(81x + 9x2) = 135

Solving
81x + 9x2 = 135

Solving for variable 'x'.

Reorder the terms:
-135 + 81x + 9x2 = 135 + -135

Combine like terms: 135 + -135 = 0
-135 + 81x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-15 + 9x + x2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(-15 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + 9x + x2 = 0

Solving
-15 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 9x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 9x + x2 = 0 + 15

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

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

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 15 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 15 + 20.25

Combine like terms: 15 + 20.25 = 35.25
20.25 + 9x + x2 = 35.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 35.25

Calculate the square root of the right side: 5.937171044

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.937171044 and -5.937171044.


Subproblem 1
x + 4.5 = 5.937171044

Simplifying
x + 4.5 = 5.937171044

Reorder the terms:
4.5 + x = 5.937171044

Solving
4.5 + x = 5.937171044

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 5.937171044 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.937171044 + -4.5
x = 5.937171044 + -4.5

Combine like terms: 5.937171044 + -4.5 = 1.437171044
x = 1.437171044

Simplifying
x = 1.437171044


Subproblem 2
x + 4.5 = -5.937171044

Simplifying
x + 4.5 = -5.937171044

Reorder the terms:
4.5 + x = -5.937171044

Solving
4.5 + x = -5.937171044

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -5.937171044 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.937171044 + -4.5
x = -5.937171044 + -4.5

Combine like terms: -5.937171044 + -4.5 = -10.437171044
x = -10.437171044

Simplifying
x = -10.437171044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.437171044, -10.437171044}
Solution
x = {1.437171044, -10.437171044}

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