The equation of a circle is x^2-6x+y^2+4y=12. Complete the square to find the centre and radius of the circle.

When we complete the square, we're looking for an equation that looks like (x-a)² + (y-b)² = r², where (a,b) is the centre and r is the radius. When we expand brackets using FOIL, the x part is (x²-2ax+a²). This means the term with x in it has a coefficient of 2a. Therefore halving it will give us a! So let's apply this to our equation. The x term has a coefficient of -6 and the y term has a coefficient of +4. Dividing these by 2 we get -3 and 2. So the centre is (-3,2)! Now since (-3)²=9 and (2)²=4 we can add these on two complete the squares: x²-6x+9-9 + y²+4x+4-4=12 (x-3)²-9 + (y+2)² -4 = 12 (x-3)² + (y+2)² = 25 (x-3)² + (y+2)² = 5² So the radius is 5!