9x^2-54x+24=0

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Solution for 9x^2-54x+24=0 equation: 


Simplifying
9x2 + -54x + 24 = 0

Reorder the terms:
24 + -54x + 9x2 = 0

Solving
24 + -54x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -18x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
8 + -18x + 3x2 = 0

Solving
8 + -18x + 3x2 = 0

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

Divide each side by '3'.
2.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -6x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -6x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -2.666666667
-6x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-6x + x2 = -2.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -2.666666667 + 9

Reorder the terms:
9 + -6x + x2 = -2.666666667 + 9

Combine like terms: -2.666666667 + 9 = 6.333333333
9 + -6x + x2 = 6.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 6.333333333

Calculate the square root of the right side: 2.516611478

Break this problem into two subproblems by setting 
(x + -3) equal to 2.516611478 and -2.516611478.


Subproblem 1
x + -3 = 2.516611478

Simplifying
x + -3 = 2.516611478

Reorder the terms:
-3 + x = 2.516611478

Solving
-3 + x = 2.516611478

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.516611478 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.516611478 + 3
x = 2.516611478 + 3

Combine like terms: 2.516611478 + 3 = 5.516611478
x = 5.516611478

Simplifying
x = 5.516611478


Subproblem 2
x + -3 = -2.516611478

Simplifying
x + -3 = -2.516611478

Reorder the terms:
-3 + x = -2.516611478

Solving
-3 + x = -2.516611478

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.516611478 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.516611478 + 3
x = -2.516611478 + 3

Combine like terms: -2.516611478 + 3 = 0.483388522
x = 0.483388522

Simplifying
x = 0.483388522


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.516611478, 0.483388522}
Solution
x = {5.516611478, 0.483388522}

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