How do you do partial fractions if the denominator has 2nd degree terms (I know the basic method)?

My textbook says:

Using partial fractions we get

Since I have to check every single thing my textbook says (it's in my genes or something):

Comparing numerator's coefficients implies that:

and therefore:

which is quite clearly wrong.

What'd I do wrong? How do I get an s term in the numerator?Thanks.