3x(x-9)=20

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Solution for 3x(x-9)=20 equation: 


Simplifying
3x(x + -9) = 20

Reorder the terms:
3x(-9 + x) = 20
(-9 * 3x + x * 3x) = 20
(-27x + 3x2) = 20

Solving
-27x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -27x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -27x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + -9x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -9x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -9x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -9x + x2 = 0 + 6.666666667
-9x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-9x + x2 = 6.666666667

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 = 6.666666667 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 6.666666667 + 20.25

Combine like terms: 6.666666667 + 20.25 = 26.916666667
20.25 + -9x + x2 = 26.916666667

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 26.916666667

Calculate the square root of the right side: 5.188127472

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.188127472 and -5.188127472.


Subproblem 1
x + -4.5 = 5.188127472

Simplifying
x + -4.5 = 5.188127472

Reorder the terms:
-4.5 + x = 5.188127472

Solving
-4.5 + x = 5.188127472

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 = 5.188127472 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 5.188127472 + 4.5
x = 5.188127472 + 4.5

Combine like terms: 5.188127472 + 4.5 = 9.688127472
x = 9.688127472

Simplifying
x = 9.688127472


Subproblem 2
x + -4.5 = -5.188127472

Simplifying
x + -4.5 = -5.188127472

Reorder the terms:
-4.5 + x = -5.188127472

Solving
-4.5 + x = -5.188127472

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 = -5.188127472 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -5.188127472 + 4.5
x = -5.188127472 + 4.5

Combine like terms: -5.188127472 + 4.5 = -0.688127472
x = -0.688127472

Simplifying
x = -0.688127472


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.688127472, -0.688127472}

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