3x^2-24x+24=0

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


Simplifying
3x2 + -24x + 24 = 0

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

Solving
24 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -8x + x2 = 0

Solving
8 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -8 + 16

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

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

Factor a perfect square on the left side:
(x + -4)(x + -4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -4) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -4 = 2.828427125

Simplifying
x + -4 = 2.828427125

Reorder the terms:
-4 + x = 2.828427125

Solving
-4 + x = 2.828427125

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 = 2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.828427125 + 4
x = 2.828427125 + 4

Combine like terms: 2.828427125 + 4 = 6.828427125
x = 6.828427125

Simplifying
x = 6.828427125


Subproblem 2
x + -4 = -2.828427125

Simplifying
x + -4 = -2.828427125

Reorder the terms:
-4 + x = -2.828427125

Solving
-4 + x = -2.828427125

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 = -2.828427125 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.828427125 + 4
x = -2.828427125 + 4

Combine like terms: -2.828427125 + 4 = 1.171572875
x = 1.171572875

Simplifying
x = 1.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.828427125, 1.171572875}
Solution
x = {6.828427125, 1.171572875}

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