SOLUTION: Find the center and the radius of the circle 3x^2+3y^2+15x-11y-10=0 algebraically,

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 3





Swap the 2nd and 3rd terms to get the terms in like letters together: 



Put the addition of one blank after the 5x and another after the
 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 5, 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 , 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  becomes 

So we now have:



And we compare that to 
 

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

If you like you can rationalize  

Edwin