1. simple question

Well, perhaps not so simple for me...but maybe for you?

How can $s^2 - 2s + 2$ be equal to $(s-1)^2 + 1$ ?

I see what's going on here but how am supposed to look at the term on the left and say "Ah! Why don't I turn it into the term on the right?"

Thanks for looking!

2. Well, since (s-1)^2 shares the s^2 and the -2s and +1 terms with RHS, the only lag would be +1, so you add that.
Or s^2-2s=s(s-1) - s. So to make it into a full square, i.e, s(s-1) - 1(s-1) = s(s-1) - s +1, so we have to subtract 1 from the LHS, i.e add 1 to the RHS.
Is this the kind of answer you are looking for?

3. Originally Posted by TheBerkeleyBoss
How can $s^2 - 2s + 2$ be equal to $(s-1)^2 + 1$ ?
Has your class covered "completing the square" yet (in particular, for finding the vertex of a parabola)?