3x(x-5)=9

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Solution for 3x(x-5)=9 equation: 


Simplifying
3x(x + -5) = 9

Reorder the terms:
3x(-5 + x) = 9
(-5 * 3x + x * 3x) = 9
(-15x + 3x2) = 9

Solving
-15x + 3x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + -15x + 3x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -15x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -5x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-3 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + -5x + x2 = 0

Solving
-3 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5x + x2 = 0 + 3
-5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5x + x2 = 3

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 3 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5x + x2 = 9.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -2.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
x + -2.5 = 3.041381265

Simplifying
x + -2.5 = 3.041381265

Reorder the terms:
-2.5 + x = 3.041381265

Solving
-2.5 + x = 3.041381265

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 3.041381265 + 2.5
x = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
x = 5.541381265

Simplifying
x = 5.541381265


Subproblem 2
x + -2.5 = -3.041381265

Simplifying
x + -2.5 = -3.041381265

Reorder the terms:
-2.5 + x = -3.041381265

Solving
-2.5 + x = -3.041381265

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -3.041381265 + 2.5
x = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
x = -0.541381265

Simplifying
x = -0.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.541381265, -0.541381265}
Solution
x = {5.541381265, -0.541381265}

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