12x^2-6x-2=0

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Solution for 12x^2-6x-2=0 equation: 


Simplifying
12x2 + -6x + -2 = 0

Reorder the terms:
-2 + -6x + 12x2 = 0

Solving
-2 + -6x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -3x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -3x + 6x2)' equal to zero and attempt to solve:

Simplifying
-1 + -3x + 6x2 = 0

Solving
-1 + -3x + 6x2 = 0

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

Divide each side by '6'.
-0.1666666667 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + -0.5x + 0.1666666667 + x2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + -0.5x + x2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + 0.1666666667
-0.5x + x2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
-0.5x + x2 = 0.1666666667

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 = 0.1666666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.1666666667 + 0.0625

Combine like terms: 0.1666666667 + 0.0625 = 0.2291666667
0.0625 + -0.5x + x2 = 0.2291666667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.2291666667

Calculate the square root of the right side: 0.478713554

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.478713554 and -0.478713554.


Subproblem 1
x + -0.25 = 0.478713554

Simplifying
x + -0.25 = 0.478713554

Reorder the terms:
-0.25 + x = 0.478713554

Solving
-0.25 + x = 0.478713554

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 = 0.478713554 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.478713554 + 0.25
x = 0.478713554 + 0.25

Combine like terms: 0.478713554 + 0.25 = 0.728713554
x = 0.728713554

Simplifying
x = 0.728713554


Subproblem 2
x + -0.25 = -0.478713554

Simplifying
x + -0.25 = -0.478713554

Reorder the terms:
-0.25 + x = -0.478713554

Solving
-0.25 + x = -0.478713554

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 = -0.478713554 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.478713554 + 0.25
x = -0.478713554 + 0.25

Combine like terms: -0.478713554 + 0.25 = -0.228713554
x = -0.228713554

Simplifying
x = -0.228713554


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.728713554, -0.228713554}
Solution
x = {0.728713554, -0.228713554}

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