3X^2-16X-24=0

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Solution for 3X^2-16X-24=0 equation: 


Simplifying
3X2 + -16X + -24 = 0

Reorder the terms:
-24 + -16X + 3X2 = 0

Solving
-24 + -16X + 3X2 = 0

Solving for variable 'X'.

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

Divide each side by '3'.
-8 + -5.333333333X + X2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -5.333333333X + 8 + X2 = 0 + 8

Reorder the terms:
-8 + 8 + -5.333333333X + X2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5.333333333X + X2 = 0 + 8
-5.333333333X + X2 = 0 + 8

Combine like terms: 0 + 8 = 8
-5.333333333X + X2 = 8

The X term is -5.333333333X.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333X + 7.111111113 + X2 = 8 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333X + X2 = 8 + 7.111111113

Combine like terms: 8 + 7.111111113 = 15.111111113
7.111111113 + -5.333333333X + X2 = 15.111111113

Factor a perfect square on the left side:
(X + -2.666666667)(X + -2.666666667) = 15.111111113

Calculate the square root of the right side: 3.887301263

Break this problem into two subproblems by setting 
(X + -2.666666667) equal to 3.887301263 and -3.887301263.


Subproblem 1
X + -2.666666667 = 3.887301263

Simplifying
X + -2.666666667 = 3.887301263

Reorder the terms:
-2.666666667 + X = 3.887301263

Solving
-2.666666667 + X = 3.887301263

Solving for variable 'X'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + X = 3.887301263 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + X = 3.887301263 + 2.666666667
X = 3.887301263 + 2.666666667

Combine like terms: 3.887301263 + 2.666666667 = 6.55396793
X = 6.55396793

Simplifying
X = 6.55396793


Subproblem 2
X + -2.666666667 = -3.887301263

Simplifying
X + -2.666666667 = -3.887301263

Reorder the terms:
-2.666666667 + X = -3.887301263

Solving
-2.666666667 + X = -3.887301263

Solving for variable 'X'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + X = -3.887301263 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + X = -3.887301263 + 2.666666667
X = -3.887301263 + 2.666666667

Combine like terms: -3.887301263 + 2.666666667 = -1.220634596
X = -1.220634596

Simplifying
X = -1.220634596


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {6.55396793, -1.220634596}

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