Completing the square

Question

Carly has just opened her own nail salon. Based on experience, she knows that her daily profit, P, in dollars, can be modeled by the relation:

P= -15x^2+240x-640, where x is the number of clients per day. How many clients should she book each day to maximize her profit?

Complete the square to determine the answer.

Answer 1

-15x^2 +240x -640

P' = -30x +240 = 0

x = 240/30 = 8 clients to max profits