3x(x-1)=9

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Solution for 3x(x-1)=9 equation:


Simplifying
3x(x + -1) = 9

Reorder the terms:
3x(-1 + x) = 9
(-1 * 3x + x * 3x) = 9
(-3x + 3x2) = 9

Solving
-3x + 3x2 = 9

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + -1x + x2) = 0

Ignore the factor 3.

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

Simplifying
-3 + -1x + x2 = 0

Solving
-3 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -1x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -1x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x + x2 = 0 + 3
-1x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1x + x2 = 3

The x term is -1x.  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.
-1x + 0.25 + x2 = 3 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + -1x + x2 = 3.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + -0.5 = 1.802775638

Simplifying
x + -0.5 = 1.802775638

Reorder the terms:
-0.5 + x = 1.802775638

Solving
-0.5 + x = 1.802775638

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 = 1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.802775638 + 0.5
x = 1.802775638 + 0.5

Combine like terms: 1.802775638 + 0.5 = 2.302775638
x = 2.302775638

Simplifying
x = 2.302775638


Subproblem 2
x + -0.5 = -1.802775638

Simplifying
x + -0.5 = -1.802775638

Reorder the terms:
-0.5 + x = -1.802775638

Solving
-0.5 + x = -1.802775638

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 = -1.802775638 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.802775638 + 0.5
x = -1.802775638 + 0.5

Combine like terms: -1.802775638 + 0.5 = -1.302775638
x = -1.302775638

Simplifying
x = -1.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.302775638, -1.302775638}
Solution
x = {2.302775638, -1.302775638}

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