6x^2-33x+24=0

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Solution for 6x^2-33x+24=0 equation: 


Simplifying
6x2 + -33x + 24 = 0

Reorder the terms:
24 + -33x + 6x2 = 0

Solving
24 + -33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -11x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -11x + 2x2)' equal to zero and attempt to solve:

Simplifying
8 + -11x + 2x2 = 0

Solving
8 + -11x + 2x2 = 0

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

Divide each side by '2'.
4 + -5.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -5.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -5.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5.5x + x2 = 0 + -4
-5.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5.5x + x2 = -4

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = -4 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = -4 + 7.5625

Combine like terms: -4 + 7.5625 = 3.5625
7.5625 + -5.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -2.75) equal to 1.887458609 and -1.887458609.


Subproblem 1
x + -2.75 = 1.887458609

Simplifying
x + -2.75 = 1.887458609

Reorder the terms:
-2.75 + x = 1.887458609

Solving
-2.75 + x = 1.887458609

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 1.887458609 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 1.887458609 + 2.75
x = 1.887458609 + 2.75

Combine like terms: 1.887458609 + 2.75 = 4.637458609
x = 4.637458609

Simplifying
x = 4.637458609


Subproblem 2
x + -2.75 = -1.887458609

Simplifying
x + -2.75 = -1.887458609

Reorder the terms:
-2.75 + x = -1.887458609

Solving
-2.75 + x = -1.887458609

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -1.887458609 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -1.887458609 + 2.75
x = -1.887458609 + 2.75

Combine like terms: -1.887458609 + 2.75 = 0.862541391
x = 0.862541391

Simplifying
x = 0.862541391


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.637458609, 0.862541391}
Solution
x = {4.637458609, 0.862541391}

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