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Okay so ladies and gentlemen what we have in this case we have x squared plus y squared plus 4x minus 10y minus seven equals zero and what they're asking us to do is find the center in the radius of the circle and then sketch the graph all right so what we're gonna have to do for this problem is what we're gonna simply do is we need to first be able to determine what if it's in our standard form of our equation of a circle so remember standard form equation of a circle looked like this X minus H squared plus y minus K squared equals R squared right yes does this look anything like that because once it's like this it's pretty easy we know that the center of the circle all right is H comma K and the radius is equal to R so as long as we can get it in this format determining what the center and the radius is is pretty simple correct did you guys agree okay so now what we need to do is we need to figure out how are we going to take it from this format to this format and there's a little bit of process that we started off the class with which we call which we call tum pleating the completing the square exactly and notice we're gonna have to go ahead and do it twice all right so x squared plus 4x plus y squared minus 10y minus seven equals zero all right okay so what we're simply going to do now is so what I did is I just rewrote it I'm sorry that's yeah so what I did is I rewrote it with my X's next to each other and my Y's next to each other so now what I can go ahead and do all right davin you got this one good so now what I can go and do is now complete the square for each one of these terms well I need to determine is there any if there is a term in front of my quadratic than I have to factor out fortunately for us we don't have any terms in front of our quadratics right so we're good so well now I can expect to take this and we're going to complete this square so I'll take my B divided by 2 which is 4 divided by 2 squared which equals 4 and then over here over here I take my B divided by 2 which is my negative 10 divided by 2 and I square it which then is going to equal 25 okay yeah all right so now remember we add each one of those into our components now I have x squared plus 4x plus 4 plus y squared minus 10y plus 25 when we complete the square what we do is we now have taken a binomial and created a perfect square trinomial all right but it's important that since we added the 4 we have to make sure that we either subtract it on the same side or add the 4 to the other side right because it's an equation so if you introduced by adding a 4 on one side you have to make sure you add it on the other side or the equation it's not going to be equal anymore so then I have to do the exact same thing for 25 now to help this problem along if you guys notice in our general format it's just X minus H squared plus y minus K squared right there's no other room for this -7 so what I'm also gonna do is add the 7 to the other side okay so I'm going to get all the numbers to those side except for my X and my y's when the perfect square trinomials now the whole reason why we again complete the square is one to create a perfect square trinomial all right and then two to be able to create a binomial squared so here we're gonna have X plus 2 squared plus y minus 5 squared equals 4 plus 25 is 29 plus 7 is going to be 36 now we know our HRK and we know our radius is going to be R all right so therefore yes no since you're adding it to the left side I'm adding it to over to the right side okay can we wait two seconds no you cancel each other out on the equation when you add the one to the left side and add it to the right side they embed they can't counter out the balance of the equation right so therefore our Center is going to be negative 2/5 and then our radius is going to equal 6 because remember it says it equals R cubed or R squared well 36 is what squared which is R which is 6 ok all right so ladies and gentlemen what I'm going to do is I'm going to leave you with some time

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