1) You know this has to be a squared term, so just look for the roots of the first and last terms. For the first term, and for the last term, . You can check either by FOIL or the Box Method and you will see that it comes out to the initial formula.
2) Once again, look for the square roots of the first and last terms. In this case, you have to sort the initial equation out so that it looks like a normal trinomial, this is what you get:
Then you just take the square roots of the first and last terms, which are 0.5x and 10y, respectively.
First, federal administrators would run an automated algorithm to divide vaccine doses nationwide, based on the size of each state's adult population. Then each state would decide how to dole out the shots to local hospitals, nursing homes and clinics.
