6x^2-54x+24=0

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Solution for 6x^2-54x+24=0 equation: 


Simplifying
6x2 + -54x + 24 = 0

Reorder the terms:
24 + -54x + 6x2 = 0

Solving
24 + -54x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -9x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(4 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -9x + x2 = 0

Solving
4 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -9x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -9x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x + x2 = 0 + -4
-9x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-9x + x2 = -4

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 = -4 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -4 + 20.25

Combine like terms: -4 + 20.25 = 16.25
20.25 + -9x + x2 = 16.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + -4.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
x + -4.5 = 4.031128874

Simplifying
x + -4.5 = 4.031128874

Reorder the terms:
-4.5 + x = 4.031128874

Solving
-4.5 + x = 4.031128874

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 = 4.031128874 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 4.031128874 + 4.5
x = 4.031128874 + 4.5

Combine like terms: 4.031128874 + 4.5 = 8.531128874
x = 8.531128874

Simplifying
x = 8.531128874


Subproblem 2
x + -4.5 = -4.031128874

Simplifying
x + -4.5 = -4.031128874

Reorder the terms:
-4.5 + x = -4.031128874

Solving
-4.5 + x = -4.031128874

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 = -4.031128874 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -4.031128874 + 4.5
x = -4.031128874 + 4.5

Combine like terms: -4.031128874 + 4.5 = 0.468871126
x = 0.468871126

Simplifying
x = 0.468871126


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.531128874, 0.468871126}
Solution
x = {8.531128874, 0.468871126}

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