First of all notice that every term is divisible by 4, so let's divide every term by 4:Let's add 31 to both sides: Let's complete the square of the last two terms on the left side. We take the coefficient of y, which is 4, multiply it by , getting 2, then we square 2, and is 4, so we add to both sides: Let's put parentheses around the last three terms on the left side and combine the terms on the right: Now factor the trinomials in the parentheses: That can be written as In fact you could have skipped the step before that. The standard form for a circle is Since you didn't have to complete the square on the x term, because you only had an term and no x-term, then to get it in the standard form you have to write as to have the standard form, so the answer is is the equation of a circle which has center (h,k) and radius r is the equation for a circle which has center (0,-2) and radius which is about 5.92 and has this graph: ---------------------------------------------- Are you sure there wasn't supposed to be an x after the -24? The reason I ask that is I don't think when you are advanced enough to be studying circles, that your teacher would still be testing you on such an elementary thing as to see whether you could combine the terms -24 and -100. So I'm going to assume you really meant: First of all notice that every term is divisible by 4, so let's divide every term by 4: Let's group the the two terms in x first and the two terms in y second, and add 25 to both sides: To complete the square of the first two terms we take the coefficient of x, which is -6, multiply it by , getting -3, then we square -3, and is 9, so we add to both sides: Let's put parentheses around the first three terms and combinethe terms on the right. Now lwt's complete the square of the last two terms on the left side. We take the coefficient of y, which is 4, multiply it by , getting 2, then we square 2, and is 4, so we add to both sides: Let's put parentheses around the last three terms on the left side and combine the terms on the right: Now factor the trinomials in the two parentheses: That can be written as In fact you could have skipped the step before that. That's the standard form for a circle which has center (h,k) and radius r is the equation for a circle which has center (3,-2) and radius which is about 6.16 and has this graph: Edwin