24x^2-100x+108=0

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Solution for 24x^2-100x+108=0 equation: 


Simplifying
24x2 + -100x + 108 = 0

Reorder the terms:
108 + -100x + 24x2 = 0

Solving
108 + -100x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + -25x + 6x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(27 + -25x + 6x2)' equal to zero and attempt to solve:

Simplifying
27 + -25x + 6x2 = 0

Solving
27 + -25x + 6x2 = 0

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

Divide each side by '6'.
4.5 + -4.166666667x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -4.166666667x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -4.166666667x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -4.166666667x + x2 = 0 + -4.5
-4.166666667x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-4.166666667x + x2 = -4.5

The x term is -4.166666667x.  Take half its coefficient (-2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
-4.166666667x + 4.340277781 + x2 = -4.5 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667x + x2 = -4.5 + 4.340277781

Combine like terms: -4.5 + 4.340277781 = -0.159722219
4.340277781 + -4.166666667x + x2 = -0.159722219

Factor a perfect square on the left side:
(x + -2.083333334)(x + -2.083333334) = -0.159722219

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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