I think I complete the square but idk Rewrite the expression $4s^2 + 28s + 45$ in the form $(cs + p)^2 + q$. What is $q$?

AnonymousConfusedGuy
Oct 20, 2017

#1**+2 **

4s^2 + 28s + 45 factor out the 4

4 [ s^2 + 7s + 45/4]

Take (1/2) of 7 = 7/2......square this = 49/4 ....add it and subtract it

4 [ s^2 + 7s + 49/4 + 45/4 - 49/4 ]

Factor the first three terms and simplify

4 [ ( s + 7/2)^2 - 1 ]

4(s + 7/2)^2 - 4

So q = -4

CPhill
Oct 20, 2017