24x^2-1080x+1584=0

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Solution for 24x^2-1080x+1584=0 equation: 


Simplifying
24x2 + -1080x + 1584 = 0

Reorder the terms:
1584 + -1080x + 24x2 = 0

Solving
1584 + -1080x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(66 + -45x + x2) = 0

Ignore the factor 24.

Subproblem 1
Set the factor '(66 + -45x + x2)' equal to zero and attempt to solve:

Simplifying
66 + -45x + x2 = 0

Solving
66 + -45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-66' to each side of the equation.
66 + -45x + -66 + x2 = 0 + -66

Reorder the terms:
66 + -66 + -45x + x2 = 0 + -66

Combine like terms: 66 + -66 = 0
0 + -45x + x2 = 0 + -66
-45x + x2 = 0 + -66

Combine like terms: 0 + -66 = -66
-45x + x2 = -66

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = -66 + 506.25

Reorder the terms:
506.25 + -45x + x2 = -66 + 506.25

Combine like terms: -66 + 506.25 = 440.25
506.25 + -45x + x2 = 440.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 440.25

Calculate the square root of the right side: 20.982135258

Break this problem into two subproblems by setting 
(x + -22.5) equal to 20.982135258 and -20.982135258.


Subproblem 1
x + -22.5 = 20.982135258

Simplifying
x + -22.5 = 20.982135258

Reorder the terms:
-22.5 + x = 20.982135258

Solving
-22.5 + x = 20.982135258

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = 20.982135258 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 20.982135258 + 22.5
x = 20.982135258 + 22.5

Combine like terms: 20.982135258 + 22.5 = 43.482135258
x = 43.482135258

Simplifying
x = 43.482135258


Subproblem 2
x + -22.5 = -20.982135258

Simplifying
x + -22.5 = -20.982135258

Reorder the terms:
-22.5 + x = -20.982135258

Solving
-22.5 + x = -20.982135258

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = -20.982135258 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -20.982135258 + 22.5
x = -20.982135258 + 22.5

Combine like terms: -20.982135258 + 22.5 = 1.517864742
x = 1.517864742

Simplifying
x = 1.517864742


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43.482135258, 1.517864742}
Solution
x = {43.482135258, 1.517864742}

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