9x^2-45x+24=0

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Solution for 9x^2-45x+24=0 equation: 


Simplifying
9x2 + -45x + 24 = 0

Reorder the terms:
24 + -45x + 9x2 = 0

Solving
24 + -45x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -15x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -15x + 3x2)' equal to zero and attempt to solve:

Simplifying
8 + -15x + 3x2 = 0

Solving
8 + -15x + 3x2 = 0

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

Divide each side by '3'.
2.666666667 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -5x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -5x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -5x + x2 = 0 + -2.666666667
-5x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-5x + x2 = -2.666666667

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 = -2.666666667 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.666666667 + 6.25

Combine like terms: -2.666666667 + 6.25 = 3.583333333
6.25 + -5x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.892969449 and -1.892969449.


Subproblem 1
x + -2.5 = 1.892969449

Simplifying
x + -2.5 = 1.892969449

Reorder the terms:
-2.5 + x = 1.892969449

Solving
-2.5 + x = 1.892969449

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 = 1.892969449 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.892969449 + 2.5
x = 1.892969449 + 2.5

Combine like terms: 1.892969449 + 2.5 = 4.392969449
x = 4.392969449

Simplifying
x = 4.392969449


Subproblem 2
x + -2.5 = -1.892969449

Simplifying
x + -2.5 = -1.892969449

Reorder the terms:
-2.5 + x = -1.892969449

Solving
-2.5 + x = -1.892969449

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 = -1.892969449 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.892969449 + 2.5
x = -1.892969449 + 2.5

Combine like terms: -1.892969449 + 2.5 = 0.607030551
x = 0.607030551

Simplifying
x = 0.607030551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.392969449, 0.607030551}
Solution
x = {4.392969449, 0.607030551}

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