0=3x^2-24x-48

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Solution for 0=3x^2-24x-48 equation: 


Simplifying
0 = 3x2 + -24x + -48

Reorder the terms:
0 = -48 + -24x + 3x2

Solving
0 = -48 + -24x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 48 = 48
48 + 24x + -3x2 = -48 + -24x + 3x2 + 48 + 24x + -3x2

Reorder the terms:
48 + 24x + -3x2 = -48 + 48 + -24x + 24x + 3x2 + -3x2

Combine like terms: -48 + 48 = 0
48 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2
48 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2

Combine like terms: -24x + 24x = 0
48 + 24x + -3x2 = 0 + 3x2 + -3x2
48 + 24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
48 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(16 + 8x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(16 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
16 + 8x + -1x2 = 0

Solving
16 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -8x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -8x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -8x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -8x + x2 = 0 + 16
-8x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-8x + x2 = 16

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 = 16 + 16

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

Combine like terms: 16 + 16 = 32
16 + -8x + x2 = 32

Factor a perfect square on the left side:
(x + -4)(x + -4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -4) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + -4 = 5.656854249

Simplifying
x + -4 = 5.656854249

Reorder the terms:
-4 + x = 5.656854249

Solving
-4 + x = 5.656854249

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 5.656854249 + 4

Combine like terms: -4 + 4 = 0
0 + x = 5.656854249 + 4
x = 5.656854249 + 4

Combine like terms: 5.656854249 + 4 = 9.656854249
x = 9.656854249

Simplifying
x = 9.656854249


Subproblem 2
x + -4 = -5.656854249

Simplifying
x + -4 = -5.656854249

Reorder the terms:
-4 + x = -5.656854249

Solving
-4 + x = -5.656854249

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -5.656854249 + 4

Combine like terms: -4 + 4 = 0
0 + x = -5.656854249 + 4
x = -5.656854249 + 4

Combine like terms: -5.656854249 + 4 = -1.656854249
x = -1.656854249

Simplifying
x = -1.656854249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.656854249, -1.656854249}
Solution
x = {9.656854249, -1.656854249}

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