Question 551225
Starting with:
P(x) = -5x^2+550x-5000
since profit is zero, replace P(x) with a zero:
0 = -5x^2+550x-5000
multiply both sides by -1:
0 = 5x^2-550x+5000
divide both sides by 5:
0 = x^2-110x+1000
factoring:
0 = (x-10)(x-100)
x = {10,100}
two solutions:
$10 and $100