We need to get it in the form  so we'll
know it has center (h,k) and radius r.

First we add 10 to both sides to get the constant off the left side:



Next we divide through by the common coefficient of x² and y² which
is 5





Put the addition of one blank after the 3x and another after the -2y since we
are going to add something to both sides



Next we calculate what goes in the first blank:

1. Multiply the coefficient of x, which is 3, by }, getting 
2. Square that value:  , so  is what goes
in the first blank, and we also add it to the right side:

  

Next we calculate what goes in the second blank:

1. Multiply the coefficient of y, which is -2, by }, getting 
2. Square that value:  , so  is what goes
in the second blank, and we also add it to the right side:



The first three terms on the left  factors as  or 

The last three terms on the left  factors as  or 

The right side  becones 

So we now have:



And we compare that to 
 

and we see that since , , and
since , . Also  so }

Edwin