3X^2-24X+4=0

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Solution for 3X^2-24X+4=0 equation: 


Simplifying
3X2 + -24X + 4 = 0

Reorder the terms:
4 + -24X + 3X2 = 0

Solving
4 + -24X + 3X2 = 0

Solving for variable 'X'.

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

Divide each side by '3'.
1.333333333 + -8X + X2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -8X + -1.333333333 + X2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -8X + X2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -8X + X2 = 0 + -1.333333333
-8X + X2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-8X + X2 = -1.333333333

The X term is -8X.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8X + 16 + X2 = -1.333333333 + 16

Reorder the terms:
16 + -8X + X2 = -1.333333333 + 16

Combine like terms: -1.333333333 + 16 = 14.666666667
16 + -8X + X2 = 14.666666667

Factor a perfect square on the left side:
(X + -4)(X + -4) = 14.666666667

Calculate the square root of the right side: 3.829708431

Break this problem into two subproblems by setting 
(X + -4) equal to 3.829708431 and -3.829708431.


Subproblem 1
X + -4 = 3.829708431

Simplifying
X + -4 = 3.829708431

Reorder the terms:
-4 + X = 3.829708431

Solving
-4 + X = 3.829708431

Solving for variable 'X'.

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

Add '4' to each side of the equation.
-4 + 4 + X = 3.829708431 + 4

Combine like terms: -4 + 4 = 0
0 + X = 3.829708431 + 4
X = 3.829708431 + 4

Combine like terms: 3.829708431 + 4 = 7.829708431
X = 7.829708431

Simplifying
X = 7.829708431


Subproblem 2
X + -4 = -3.829708431

Simplifying
X + -4 = -3.829708431

Reorder the terms:
-4 + X = -3.829708431

Solving
-4 + X = -3.829708431

Solving for variable 'X'.

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

Add '4' to each side of the equation.
-4 + 4 + X = -3.829708431 + 4

Combine like terms: -4 + 4 = 0
0 + X = -3.829708431 + 4
X = -3.829708431 + 4

Combine like terms: -3.829708431 + 4 = 0.170291569
X = 0.170291569

Simplifying
X = 0.170291569


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {7.829708431, 0.170291569}

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