 This is part two of the circles. Now we're going to go from expanded form into that standard form that we've already looked at. And we need completing the square to be able to do that. First thing we want to do here is we want to get the x's together and y's together and then we want it equal to any constants that we have. So we want to move all the constants to the other side. So we need to take the six and put it to the other side and then I need to group these two things together and I need to group these two things together. And again like I said the six needs to go over here. So we have x squared plus 6x and then we have plus y squared minus 8y and that's going to be equal to positive six. Now when we complete the square we really need to have a little bit of space here. So let's rewrite this as x squared plus 6x plus sum number because that will complete that square plus y squared minus 8y plus sum number. And then switching my colors around here. That will be equal to the six that we already have. But if I add something to one side remember I have to add it to the other side so I have to add those two constants on this side as well. So how do I know what goes in the box? Well inside the box is really going to be equal to half of the middle term squared or b over 2 squared. And then we need to figure out what that is. We have 6 divided by 2 equal 3 and 3 squared is equal to 9. So we have 9 here but we have to add it to this side as well. And then we have negative 8 divided by 2 which is equal to negative 4 and negative 4 squared is equal to because remember it's the negative inside. That didn't look very good. Try that again. Negative 4 being squared is going to be equal to 16 and that's what we're going to add to both sides. And now we just have to get it in the right form. Well when we did this we built a perfect trinomial square. And perfect trinomial squares then end up being the first term. Remember you would factor x and x. So the first term is going to be the first term on squared. And it so happens that this last number right here is going to be that b over 2. So let me put that over here. That's just b over 2. Because if I unsquare 9 I get to 3. If I double 3 I get to 6. And it was a positive 3 so x plus 3 quantity squared. And then we do the same thing with the y's. Well I unsquare the y squared and it's just y. And I either take half of the 8 to know what I'm going to add or unsquare the 16 but it's better to take half of the negative 8 so you get the right sign. So half of the negative 8 is minus 4. And then we're going to square that. And then we just add all this up. 15 plus 16 is going to be equal to 31. Then it says find the center and the radius. So hk is equal to if it's x plus 3 that means it was a negative 3 that we subtracted. And if it's x minus 4 that means it was a positive 4 that we subtracted. And then the radius is equal to 31 but that's radius squared so I have to take the square root and we have the square root of 31. Okay so let's try this again. I've got x squared plus 6x plus some number plus y squared plus 4y plus some number. And that's going to be equal to negative 12 and then plus the two numbers that we are going to add to both sides. That's step one. Now step two put this in purple. We take 6 divided by 2 and that's equal to 3 and 3 squared is equal to 9. So which one of those did we put in there? The 3 squared. And then from here we say x and the 3 minus 3 quantity squared. So again the 9 went here and the 3 went here. And then plus our y. Oh let's add the 9 to the other side while I'm at it. So don't forget. So y 4 half of 4 is 2 and 2 squared is 4. So up here we're going to add 4 to both sides because that's the 2 squared. But it was y minus a 2. And then if we add 9 and 4 is going to be 13 minus 12. We'll just give us 1. So we went the center. HK is 3 and 2. And R is the square root of 1 which is just 1.