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hm, not quite, do you know how to complete the square?
ok, just look at the x part (x^2 + 2x) if you add 1, you get x^2 + 2x + 1 which equals (x+1)^2 do you understand where the 1 comes from?
I mean, do you understand why I added 1?
Nope, I didn't do anything to the 2x I only added 1 so I could rewrite (x^2 + 2x) in the form (x+1)^2
(x^2 + 2x + 1) = (x+1)^2
(a+b)^2 = (a^2 + 2ab + b^2), have you seen this formula before?
Well, it's kinda hard to explain, but you want to rewrite (x^2 + 2x) in the form (a+b)^2 or (a-b)^2 by adding a number
can you try rewriting (y^2 + 4y + ___) in the form (y+b)^2? can you try filling in the blank so you get an expression in the form (y+b)^2
in other words, what value should we add to make the expression equal to (y+b)^2 where b is a constant? i'm sorry, this is hard to explain D:
ok, I'll give you a hint: we can add a number to y^2 + 4y to get (y+2)^2 what is that number?
hint: try expanding (y+2)^2 = (y+2)(y+2)
what is (y+2)(y+2)?
yup! and how do we get from y^2 + 4y to y^2 + 4y + 4?
this might be helpful in explaining the concept, http://www.purplemath.com/modules/sqrcircle.htm
nope, you add 4 to the expression
alright, I think I might have a better way to explain this...
ok, after all the math we just did, we have: (x+1)^2 + (y+2)^2 = 20 + 4 + 1 remember, we added 4 and 1 to the left side, so we must add 4 and 1 to the right side
(x+1)^2 + (y+2)^2 = 25, are you with me so far?
alright, you know that the general equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where r is the radius and (h,k) is the center, right?
can you tell me what h, k, and r are, based on what we just found out?
not quite, check your math again check the signs on h and k, and check r r^2 = 25, so what is r?
right, and what are h and k?
not quite! -h = 1 -k = 2 so, what are h and k?
yup! make sure to check the signs! so, can you now tell me what the center and radius are?
yup, good job ~
that's it, look at the question again: "find the center and the radius of the circle", so you're done
actually I need to go pretty soon, can I just outline my steps for you? x^2 + 2x + y^2 + 4y = 20 (x^2+2x) + (y^2 + 4y) = 20 (x^2 + 2x + 1) + (y^2 +4y + 4) = 20 + 4 + 1 = 25 (x+1)^2 + (y+2)^2 = 25 h = -1 k = -2 r = 5
ok fantastic! you did perfectly, great job ~