1.5x^2-24x-24=0

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Solution for 1.5x^2-24x-24=0 equation: 


Simplifying
1.5x2 + -24x + -24 = 0

Reorder the terms:
-24 + -24x + 1.5x2 = 0

Solving
-24 + -24x + 1.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.5'.
-16 + -16x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -16x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -16x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -16x + x2 = 0 + 16
-16x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-16x + x2 = 16

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 16 + 64

Reorder the terms:
64 + -16x + x2 = 16 + 64

Combine like terms: 16 + 64 = 80
64 + -16x + x2 = 80

Factor a perfect square on the left side:
(x + -8)(x + -8) = 80

Calculate the square root of the right side: 8.94427191

Break this problem into two subproblems by setting 
(x + -8) equal to 8.94427191 and -8.94427191.


Subproblem 1
x + -8 = 8.94427191

Simplifying
x + -8 = 8.94427191

Reorder the terms:
-8 + x = 8.94427191

Solving
-8 + x = 8.94427191

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 8.94427191 + 8

Combine like terms: -8 + 8 = 0
0 + x = 8.94427191 + 8
x = 8.94427191 + 8

Combine like terms: 8.94427191 + 8 = 16.94427191
x = 16.94427191

Simplifying
x = 16.94427191


Subproblem 2
x + -8 = -8.94427191

Simplifying
x + -8 = -8.94427191

Reorder the terms:
-8 + x = -8.94427191

Solving
-8 + x = -8.94427191

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -8.94427191 + 8

Combine like terms: -8 + 8 = 0
0 + x = -8.94427191 + 8
x = -8.94427191 + 8

Combine like terms: -8.94427191 + 8 = -0.94427191
x = -0.94427191

Simplifying
x = -0.94427191


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.94427191, -0.94427191}

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