3x^2-24x+8=0

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Solution for 3x^2-24x+8=0 equation: 


Simplifying
3x2 + -24x + 8 = 0

Reorder the terms:
8 + -24x + 3x2 = 0

Solving
8 + -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'.
2.666666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -8x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -8x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -8x + x2 = 0 + -2.666666667
-8x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-8x + x2 = -2.666666667

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 = -2.666666667 + 16

Reorder the terms:
16 + -8x + x2 = -2.666666667 + 16

Combine like terms: -2.666666667 + 16 = 13.333333333
16 + -8x + x2 = 13.333333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 13.333333333

Calculate the square root of the right side: 3.651483717

Break this problem into two subproblems by setting 
(x + -4) equal to 3.651483717 and -3.651483717.


Subproblem 1
x + -4 = 3.651483717

Simplifying
x + -4 = 3.651483717

Reorder the terms:
-4 + x = 3.651483717

Solving
-4 + x = 3.651483717

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 = 3.651483717 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.651483717 + 4
x = 3.651483717 + 4

Combine like terms: 3.651483717 + 4 = 7.651483717
x = 7.651483717

Simplifying
x = 7.651483717


Subproblem 2
x + -4 = -3.651483717

Simplifying
x + -4 = -3.651483717

Reorder the terms:
-4 + x = -3.651483717

Solving
-4 + x = -3.651483717

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 = -3.651483717 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.651483717 + 4
x = -3.651483717 + 4

Combine like terms: -3.651483717 + 4 = 0.348516283
x = 0.348516283

Simplifying
x = 0.348516283


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.651483717, 0.348516283}

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