8X^2-12X+2=0

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Solution for 8X^2-12X+2=0 equation: 


Simplifying
8X2 + -12X + 2 = 0

Reorder the terms:
2 + -12X + 8X2 = 0

Solving
2 + -12X + 8X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6X + 4X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -6X + 4X2)' equal to zero and attempt to solve:

Simplifying
1 + -6X + 4X2 = 0

Solving
1 + -6X + 4X2 = 0

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

Divide each side by '4'.
0.25 + -1.5X + X2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.5X + -0.25 + X2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.5X + X2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.5X + X2 = 0 + -0.25
-1.5X + X2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.5X + X2 = -0.25

The X term is -1.5X.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5X + 0.5625 + X2 = -0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5X + X2 = -0.25 + 0.5625

Combine like terms: -0.25 + 0.5625 = 0.3125
0.5625 + -1.5X + X2 = 0.3125

Factor a perfect square on the left side:
(X + -0.75)(X + -0.75) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(X + -0.75) equal to 0.559016994 and -0.559016994.


Subproblem 1
X + -0.75 = 0.559016994

Simplifying
X + -0.75 = 0.559016994

Reorder the terms:
-0.75 + X = 0.559016994

Solving
-0.75 + X = 0.559016994

Solving for variable 'X'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + X = 0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + X = 0.559016994 + 0.75
X = 0.559016994 + 0.75

Combine like terms: 0.559016994 + 0.75 = 1.309016994
X = 1.309016994

Simplifying
X = 1.309016994


Subproblem 2
X + -0.75 = -0.559016994

Simplifying
X + -0.75 = -0.559016994

Reorder the terms:
-0.75 + X = -0.559016994

Solving
-0.75 + X = -0.559016994

Solving for variable 'X'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + X = -0.559016994 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + X = -0.559016994 + 0.75
X = -0.559016994 + 0.75

Combine like terms: -0.559016994 + 0.75 = 0.190983006
X = 0.190983006

Simplifying
X = 0.190983006


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.309016994, 0.190983006}
Solution
X = {1.309016994, 0.190983006}

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