24x^2-88x+224=0

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Solution for 24x^2-88x+224=0 equation: 


Simplifying
24x2 + -88x + 224 = 0

Reorder the terms:
224 + -88x + 24x2 = 0

Solving
224 + -88x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(28 + -11x + 3x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(28 + -11x + 3x2)' equal to zero and attempt to solve:

Simplifying
28 + -11x + 3x2 = 0

Solving
28 + -11x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -3.666666667x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -3.666666667x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + -9.333333333
-3.666666667x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-3.666666667x + x2 = -9.333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -9.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -9.333333333 + 3.361111114

Combine like terms: -9.333333333 + 3.361111114 = -5.972222219
3.361111114 + -3.666666667x + x2 = -5.972222219

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = -5.972222219

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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