-24x^2+192x-512=0

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Solution for -24x^2+192x-512=0 equation: 


Simplifying
-24x2 + 192x + -512 = 0

Reorder the terms:
-512 + 192x + -24x2 = 0

Solving
-512 + 192x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-64 + 24x + -3x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-64 + 24x + -3x2)' equal to zero and attempt to solve:

Simplifying
-64 + 24x + -3x2 = 0

Solving
-64 + 24x + -3x2 = 0

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

Divide each side by '-3'.
21.33333333 + -8x + x2 = 0

Move the constant term to the right:

Add '-21.33333333' to each side of the equation.
21.33333333 + -8x + -21.33333333 + x2 = 0 + -21.33333333

Reorder the terms:
21.33333333 + -21.33333333 + -8x + x2 = 0 + -21.33333333

Combine like terms: 21.33333333 + -21.33333333 = 0.00000000
0.00000000 + -8x + x2 = 0 + -21.33333333
-8x + x2 = 0 + -21.33333333

Combine like terms: 0 + -21.33333333 = -21.33333333
-8x + x2 = -21.33333333

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -21.33333333 + 16

Reorder the terms:
16 + -8x + x2 = -21.33333333 + 16

Combine like terms: -21.33333333 + 16 = -5.33333333
16 + -8x + x2 = -5.33333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = -5.33333333

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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