 This is part two of the circle. 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 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 6x plus 6x plus 6x plus 6x plus 6x plus 6x 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 6 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 equals 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 unsquared, 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 it, negative 8 is minus 4, and then we're going to square that, and then we just add all of 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 1. Now, step 2. So if we finish off the x's, we take half of our middle term, half of b, which is 6 divided by 2 is 3, and then we'd square that to add to both sides, so 3 squared is going to be 9 that we're going to be adding to both sides, so we add it here, and we add it here, and if we continue with the x's, then remember now we have made the perfect trinomial square, and that means that we have a binomial square that comes out of it, x times x, bx squared, so there's that, and then the 9 would be 3 times 3, or half of 6 was the 3, and it was a positive 6, so it's a positive 3, and then we come and do the same thing with our y's, and we say half of the middle term, 4 divided by 2 is going to be 2, and then we square that, which is going to be 4, so we're going to add 4 to both sides, and then we say plus our binomial squared, and then we get y times y squared, and then the n squared of the 4, or think of b over 2, so now we're going to have 2, and it was a positive 4 in the middle here, so we're going to have a positive, this sign should always be the same, and then we just have to add and see what we have, so 9 and 4 is going to be 13 minus 12 will be equal to 1, so then s is for the center, and that's going to be hk, which is the opposite sign, remember, so it's negative 3 for h, and negative 2 for k. Our squared is equal to 1, so that makes r equal to the square root of 1, which we know to be 1. Here's our r, and here's our center.