48x^2-24x-4=0

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Solution for 48x^2-24x-4=0 equation: 


Simplifying
48x2 + -24x + -4 = 0

Reorder the terms:
-4 + -24x + 48x2 = 0

Solving
-4 + -24x + 48x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -6x + 12x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1 + -6x + 12x2)' equal to zero and attempt to solve:

Simplifying
-1 + -6x + 12x2 = 0

Solving
-1 + -6x + 12x2 = 0

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

Divide each side by '12'.
-0.08333333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + -0.5x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + -0.5x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + -0.5x + x2 = 0 + 0.08333333333
-0.5x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
-0.5x + x2 = 0.08333333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.08333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.08333333333 + 0.0625

Combine like terms: 0.08333333333 + 0.0625 = 0.14583333333
0.0625 + -0.5x + x2 = 0.14583333333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.14583333333

Calculate the square root of the right side: 0.381881308

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.381881308 and -0.381881308.


Subproblem 1
x + -0.25 = 0.381881308

Simplifying
x + -0.25 = 0.381881308

Reorder the terms:
-0.25 + x = 0.381881308

Solving
-0.25 + x = 0.381881308

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.381881308 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.381881308 + 0.25
x = 0.381881308 + 0.25

Combine like terms: 0.381881308 + 0.25 = 0.631881308
x = 0.631881308

Simplifying
x = 0.631881308


Subproblem 2
x + -0.25 = -0.381881308

Simplifying
x + -0.25 = -0.381881308

Reorder the terms:
-0.25 + x = -0.381881308

Solving
-0.25 + x = -0.381881308

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.381881308 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.381881308 + 0.25
x = -0.381881308 + 0.25

Combine like terms: -0.381881308 + 0.25 = -0.131881308
x = -0.131881308

Simplifying
x = -0.131881308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.631881308, -0.131881308}
Solution
x = {0.631881308, -0.131881308}

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