Question

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?

Answer 1

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

Answer 2

So, how do you complete the square?

Answer 3

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

Answer 4

the procedure is to take half the coefficient of the linear term (the x-term), which is half of the 2 then square it... and that's what you add.
here's an example..