Question

A piece of equipment has cost function C(x)=50x^2 + 1000 and its revenue
function is R(x)= 500x - x^2, where x is in thousands of items. What is the
least number of items that must be sold in order to break even?

50x^2 + 1000 = 500x - x^2
50x^2 + x^2 + 500= 0
51x^2 + 500 = 0

Do I just do -b/2a = -500/102= -250/51? What do I do next?

Answer 1

well, you should see right off that since 51x^2 is always positive, you can never have 51x^2 = -500.

So, let's see what happened.

50x^2 + 1000 = 500x - x^2
51x^2 - 500x + 1000 = 0

Now just use the quadratic formula to find the roots.

Answer 2

wow that was a silly mistake I didn't see the x next to 500 and thought I could just subtract it from 1000

thank you!