Will fan and medal!!

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Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit. x2 + 2x + y2 + 4y = 20
\[x^2+2x+y^2+4y=20\]

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I know I have to complete the square but I have no clue how to do it.
convert it to the form (x - a)^2 + (y - b)^2 = r^2 complete the square x^2 + 2x and y^2 + 4y
We use (h-k)^2+(y-k)^2=r^2 but it's the same thing as the form you gave me.
x^2 + 2x + y^2 + 4y = 20 (x + 1)^2 - 1 + (y + 2)^2 - 4 = 20 to complete the square you take half of the coefficient of x then you have to subtract this value squared (x + 1)^2 = x^2 + 2x + 1 - so you have to subtract 1^2 from this to make x^2 + 2x
(x + 1)^2 + (y + 2)^2 = 20+1 + 4 = 25 so if you compare this with the general equation you'll see that center = (-1,-2) and radius = sqrt25 = 5
Thank you so much. I have one more question if you dont mind?
well i must go in 10 minutes so we'll see how much i can do in that time
Prove that the two circles shown below are similar.
1 Attachment
I know that all circles are similar, but how do I prove it?
oh must go now I'm sure jhannybean can help
Okay thank you!
\[x^2 + 2x + y^2 + 4y = 20\]\[(x^2+2x) + (y^2+4y)=20\]\[(x^2+2x+\color{red}{1}) +(y^2+4y+\color{red}{4})=20+\color{red}{1}+\color{red}{4}\]\[(x+1)^2+(y+2)^2=25~~~\checkmark \]
Haha you dont have to @welshfella
@Jhannybean Could you help with the circle question? It's my last one. :/
hint: try creating triangles within the circles and then using their ratios in comparison.
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So once i have the ratios what do i do?
If we compare al the sides in a ratio, we would see it has a proportional relationship
First find the hypotenuse of both triangles, the smaller triangle having a hypotenuse of x. and the bigger one having hypotenuse of y. \[c_1 : x^2= 2^2+2^2 = 8 \iff x=\sqrt{8}\]\[c_2 : y^2=5^2+5^2 = 50 \iff y=\sqrt{50}\]
What about dilations? Couldn't we see if they are similar that way?
Then we can say by the SSS theorem, \[\frac{2}{5} = \frac{\sqrt{8}}{\sqrt{50}}\]
Hmm..i'm not really familiar with dilations! sorry.
Okay well thank you!
@cwrw238 could you help me understand dilations? :)
I understand the way you did it, and it makes perfect sense, so no worries. :) thank you for your help!
Oh cool! no problem.

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