6x(9+x)=162

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Solution for 6x(9+x)=162 equation: 


Simplifying
6x(9 + x) = 162
(9 * 6x + x * 6x) = 162
(54x + 6x2) = 162

Solving
54x + 6x2 = 162

Solving for variable 'x'.

Reorder the terms:
-162 + 54x + 6x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-162 + 54x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-27 + 9x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-27 + 9x + x2)' equal to zero and attempt to solve:

Simplifying
-27 + 9x + x2 = 0

Solving
-27 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 9x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + 9x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 9x + x2 = 0 + 27
9x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
9x + x2 = 27

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 = 27 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 27 + 20.25

Combine like terms: 27 + 20.25 = 47.25
20.25 + 9x + x2 = 47.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.873863542 and -6.873863542.


Subproblem 1
x + 4.5 = 6.873863542

Simplifying
x + 4.5 = 6.873863542

Reorder the terms:
4.5 + x = 6.873863542

Solving
4.5 + x = 6.873863542

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 = 6.873863542 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.873863542 + -4.5
x = 6.873863542 + -4.5

Combine like terms: 6.873863542 + -4.5 = 2.373863542
x = 2.373863542

Simplifying
x = 2.373863542


Subproblem 2
x + 4.5 = -6.873863542

Simplifying
x + 4.5 = -6.873863542

Reorder the terms:
4.5 + x = -6.873863542

Solving
4.5 + x = -6.873863542

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 = -6.873863542 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.873863542 + -4.5
x = -6.873863542 + -4.5

Combine like terms: -6.873863542 + -4.5 = -11.373863542
x = -11.373863542

Simplifying
x = -11.373863542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.373863542, -11.373863542}
Solution
x = {2.373863542, -11.373863542}

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