How does (x^2 -2x) + (y^2+4y)=7 become
(x^2-2x+1)+(y^2 +4y+4)=7+1+4?
Where specifically do the 1 and 4 come from?

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the 1 and the 4 in the right side came from completing the square on the left side.

So, how do you complete the square?

(x^2 - 2x + ???)
what needs to be in place of ??? in order (no pun) to write in this form: (x - #)^2

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