-3x^2-8x-24=0

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Solution for -3x^2-8x-24=0 equation: 


Simplifying
-3x2 + -8x + -24 = 0

Reorder the terms:
-24 + -8x + -3x2 = 0

Solving
-24 + -8x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 8x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(24 + 8x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + 8x + 3x2 = 0

Solving
24 + 8x + 3x2 = 0

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

Divide each side by '3'.
8 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 2.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 2.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 2.666666667x + x2 = 0 + -8
2.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
2.666666667x + x2 = -8

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -8 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -8 + 1.777777780

Combine like terms: -8 + 1.777777780 = -6.22222222
1.777777780 + 2.666666667x + x2 = -6.22222222

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -6.22222222

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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