9x^2-12x-48=0

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Solution for 9x^2-12x-48=0 equation: 


Simplifying
9x2 + -12x + -48 = 0

Reorder the terms:
-48 + -12x + 9x2 = 0

Solving
-48 + -12x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + -4x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-16 + -4x + 3x2)' equal to zero and attempt to solve:

Simplifying
-16 + -4x + 3x2 = 0

Solving
-16 + -4x + 3x2 = 0

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

Divide each side by '3'.
-5.333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -1.333333333x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -1.333333333x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 5.333333333
-1.333333333x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-1.333333333x + x2 = 5.333333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 5.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 5.333333333 + 0.4444444442

Combine like terms: 5.333333333 + 0.4444444442 = 5.7777777772
0.4444444442 + -1.333333333x + x2 = 5.7777777772

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 5.7777777772

Calculate the square root of the right side: 2.40370085

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 2.40370085 and -2.40370085.


Subproblem 1
x + -0.6666666665 = 2.40370085

Simplifying
x + -0.6666666665 = 2.40370085

Reorder the terms:
-0.6666666665 + x = 2.40370085

Solving
-0.6666666665 + x = 2.40370085

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 2.40370085 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 2.40370085 + 0.6666666665
x = 2.40370085 + 0.6666666665

Combine like terms: 2.40370085 + 0.6666666665 = 3.0703675165
x = 3.0703675165

Simplifying
x = 3.0703675165


Subproblem 2
x + -0.6666666665 = -2.40370085

Simplifying
x + -0.6666666665 = -2.40370085

Reorder the terms:
-0.6666666665 + x = -2.40370085

Solving
-0.6666666665 + x = -2.40370085

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -2.40370085 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -2.40370085 + 0.6666666665
x = -2.40370085 + 0.6666666665

Combine like terms: -2.40370085 + 0.6666666665 = -1.7370341835
x = -1.7370341835

Simplifying
x = -1.7370341835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.0703675165, -1.7370341835}
Solution
x = {3.0703675165, -1.7370341835}

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