12X^2-48X+34=0

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Solution for 12X^2-48X+34=0 equation: 


Simplifying
12X2 + -48X + 34 = 0

Reorder the terms:
34 + -48X + 12X2 = 0

Solving
34 + -48X + 12X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -24X + 6X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + -24X + 6X2)' equal to zero and attempt to solve:

Simplifying
17 + -24X + 6X2 = 0

Solving
17 + -24X + 6X2 = 0

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

Divide each side by '6'.
2.833333333 + -4X + X2 = 0

Move the constant term to the right:

Add '-2.833333333' to each side of the equation.
2.833333333 + -4X + -2.833333333 + X2 = 0 + -2.833333333

Reorder the terms:
2.833333333 + -2.833333333 + -4X + X2 = 0 + -2.833333333

Combine like terms: 2.833333333 + -2.833333333 = 0.000000000
0.000000000 + -4X + X2 = 0 + -2.833333333
-4X + X2 = 0 + -2.833333333

Combine like terms: 0 + -2.833333333 = -2.833333333
-4X + X2 = -2.833333333

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 = -2.833333333 + 4

Reorder the terms:
4 + -4X + X2 = -2.833333333 + 4

Combine like terms: -2.833333333 + 4 = 1.166666667
4 + -4X + X2 = 1.166666667

Factor a perfect square on the left side:
(X + -2)(X + -2) = 1.166666667

Calculate the square root of the right side: 1.08012345

Break this problem into two subproblems by setting 
(X + -2) equal to 1.08012345 and -1.08012345.


Subproblem 1
X + -2 = 1.08012345

Simplifying
X + -2 = 1.08012345

Reorder the terms:
-2 + X = 1.08012345

Solving
-2 + X = 1.08012345

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 = 1.08012345 + 2

Combine like terms: -2 + 2 = 0
0 + X = 1.08012345 + 2
X = 1.08012345 + 2

Combine like terms: 1.08012345 + 2 = 3.08012345
X = 3.08012345

Simplifying
X = 3.08012345


Subproblem 2
X + -2 = -1.08012345

Simplifying
X + -2 = -1.08012345

Reorder the terms:
-2 + X = -1.08012345

Solving
-2 + X = -1.08012345

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 = -1.08012345 + 2

Combine like terms: -2 + 2 = 0
0 + X = -1.08012345 + 2
X = -1.08012345 + 2

Combine like terms: -1.08012345 + 2 = 0.91987655
X = 0.91987655

Simplifying
X = 0.91987655


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.08012345, 0.91987655}
Solution
X = {3.08012345, 0.91987655}

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