SOLUTION: Determine whether the equation represents a circle, a point, or has no graph. If the equation is that of a circle, find its center and radius. x^2+y^2+72=12x

                x² + y² + 72 = 12x

If it has a graph at all it would be a circle since it has both
x² and y² terms with the same coefficient when on the same side
of the equation.  So we'll try to get it into the form of a
circle, which is

             (x-h)² + (y-k)² = r²



                x² + y² + 72 = 12x

Rearrange by subtracting 12x from both sides,
and put the subtacted 12x next to the x² term:

          x² - 12x + y² + 72 = 0

Subtract 72 from both sides:

               x² - 12x + y² = -72 

Complete the square by taking  of -12, the coefficient of x,
which gives -6, then square -6 to get +36, and add 36 to both
sides:

          x² - 12x + 36 + y² = -72 + 36

Factor the first three terms, x² - 12x + 36, as (x - 6)(x - 6) which 
can be written (x - 6)²

               (x - 6)² + y² = -72 + 36

Write y² as (y - 0)² and combine the terms on the right

         (x - 6)² + (y - 0)² = -36
 
oh, oh!  There can be no graph because the terms on the left are
squares which are both non-negative, making their sum non-negative, 
yet the term on the right is negative,  So this cannot be the equation 
of any graph.

Edwin