6x^2-72x+16=0

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Solution for 6x^2-72x+16=0 equation: 


Simplifying
6x2 + -72x + 16 = 0

Reorder the terms:
16 + -72x + 6x2 = 0

Solving
16 + -72x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -36x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -36x + 3x2)' equal to zero and attempt to solve:

Simplifying
8 + -36x + 3x2 = 0

Solving
8 + -36x + 3x2 = 0

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

Divide each side by '3'.
2.666666667 + -12x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -12x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -12x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -12x + x2 = 0 + -2.666666667
-12x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-12x + x2 = -2.666666667

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -2.666666667 + 36

Reorder the terms:
36 + -12x + x2 = -2.666666667 + 36

Combine like terms: -2.666666667 + 36 = 33.333333333
36 + -12x + x2 = 33.333333333

Factor a perfect square on the left side:
(x + -6)(x + -6) = 33.333333333

Calculate the square root of the right side: 5.773502692

Break this problem into two subproblems by setting 
(x + -6) equal to 5.773502692 and -5.773502692.


Subproblem 1
x + -6 = 5.773502692

Simplifying
x + -6 = 5.773502692

Reorder the terms:
-6 + x = 5.773502692

Solving
-6 + x = 5.773502692

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 5.773502692 + 6

Combine like terms: -6 + 6 = 0
0 + x = 5.773502692 + 6
x = 5.773502692 + 6

Combine like terms: 5.773502692 + 6 = 11.773502692
x = 11.773502692

Simplifying
x = 11.773502692


Subproblem 2
x + -6 = -5.773502692

Simplifying
x + -6 = -5.773502692

Reorder the terms:
-6 + x = -5.773502692

Solving
-6 + x = -5.773502692

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -5.773502692 + 6

Combine like terms: -6 + 6 = 0
0 + x = -5.773502692 + 6
x = -5.773502692 + 6

Combine like terms: -5.773502692 + 6 = 0.226497308
x = 0.226497308

Simplifying
x = 0.226497308


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.773502692, 0.226497308}
Solution
x = {11.773502692, 0.226497308}

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