6x^2-6x-8=0

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Solution for 6x^2-6x-8=0 equation: 


Simplifying
6x2 + -6x + -8 = 0

Reorder the terms:
-8 + -6x + 6x2 = 0

Solving
-8 + -6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -3x + 3x2) = 0

Ignore the factor 2.

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

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

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

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

Divide each side by '3'.
-1.333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + 1.333333333
-1x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1x + x2 = 1.333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.333333333 + 0.25

Combine like terms: 1.333333333 + 0.25 = 1.583333333
0.25 + -1x + x2 = 1.583333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.258305739 and -1.258305739.


Subproblem 1
x + -0.5 = 1.258305739

Simplifying
x + -0.5 = 1.258305739

Reorder the terms:
-0.5 + x = 1.258305739

Solving
-0.5 + x = 1.258305739

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.258305739 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.258305739 + 0.5
x = 1.258305739 + 0.5

Combine like terms: 1.258305739 + 0.5 = 1.758305739
x = 1.758305739

Simplifying
x = 1.758305739


Subproblem 2
x + -0.5 = -1.258305739

Simplifying
x + -0.5 = -1.258305739

Reorder the terms:
-0.5 + x = -1.258305739

Solving
-0.5 + x = -1.258305739

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.258305739 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.258305739 + 0.5
x = -1.258305739 + 0.5

Combine like terms: -1.258305739 + 0.5 = -0.758305739
x = -0.758305739

Simplifying
x = -0.758305739


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.758305739, -0.758305739}
Solution
x = {1.758305739, -0.758305739}

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