Under what conditions can a quadratic function be a perfect square?

Question

Also..
A stone is thrown vertically upward at a speed of 40m/s. How long does it take to reach a height of 90m?

I ended up with a quadratic of t^2-8t+18 which cannot be factored...So is the answer that the stone doesn't reach a height of 90m?

Another question...
A hockey player shoots a puck from his own end of the ice with an initial speed of 10 m/s. The ice surface is 60 m long and produces a deceleration of 1.0m/s^2 on the sliding puck.
a) Will the puck travel the length of the ice?
b) With what speed will it reach the far end of the ice OR how far from the end of the ice will it come to rest?

I think I used the wrong equation.
I used V2^2 = V1^2 + 2ad
And solved for distance to get 50 m which indicates that the puck didn't travel the length of the ice. But I have a feeling I did it wrong since I'm also supposed to use a kinematic equation for the second question rather than just subtraction.

Thanks!