12x^2-48x-16=0

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Solution for 12x^2-48x-16=0 equation: 


Simplifying
12x2 + -48x + -16 = 0

Reorder the terms:
-16 + -48x + 12x2 = 0

Solving
-16 + -48x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -12x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-4 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + -12x + 3x2 = 0

Solving
-4 + -12x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -4x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -4x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -4x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + 1.333333333
-4x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-4x + x2 = 1.333333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.333333333 + 4

Reorder the terms:
4 + -4x + x2 = 1.333333333 + 4

Combine like terms: 1.333333333 + 4 = 5.333333333
4 + -4x + x2 = 5.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(x + -2) equal to 2.309401077 and -2.309401077.


Subproblem 1
x + -2 = 2.309401077

Simplifying
x + -2 = 2.309401077

Reorder the terms:
-2 + x = 2.309401077

Solving
-2 + x = 2.309401077

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.309401077 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.309401077 + 2
x = 2.309401077 + 2

Combine like terms: 2.309401077 + 2 = 4.309401077
x = 4.309401077

Simplifying
x = 4.309401077


Subproblem 2
x + -2 = -2.309401077

Simplifying
x + -2 = -2.309401077

Reorder the terms:
-2 + x = -2.309401077

Solving
-2 + x = -2.309401077

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.309401077 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.309401077 + 2
x = -2.309401077 + 2

Combine like terms: -2.309401077 + 2 = -0.309401077
x = -0.309401077

Simplifying
x = -0.309401077


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.309401077, -0.309401077}
Solution
x = {4.309401077, -0.309401077}

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