SOLUTION: I have been working on this math problem for the past 2 hours and is having a difficult time with it. Can anyone please help me. p(x)= -.1x^2+50x-300, where x is the number of i

Algebra ->  Average -> SOLUTION: I have been working on this math problem for the past 2 hours and is having a difficult time with it. Can anyone please help me. p(x)= -.1x^2+50x-300, where x is the number of i      Log On


   

Question 580348: I have been working on this math problem for the past 2 hours and is having a difficult time with it. Can anyone please help me.
p(x)= -.1x^2+50x-300, where x is the number of items sold, x>0.
Please and thank you
Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!
p(x)= -.1x^2+50x-300, where x is the number of items sold, x>0.
what do you want to know? P given a certain value of x? or if P(x) = some value, find x??
You haven't asked a question yet.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.1x%5E2%2B50x%2B-300+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2850%29%5E2-4%2A-0.1%2A-300=2380.

Discriminant d=2380 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-50%2B-sqrt%28+2380+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2850%29%2Bsqrt%28+2380+%29%29%2F2%5C-0.1+=+6.07378164699064
x%5B2%5D+=+%28-%2850%29-sqrt%28+2380+%29%29%2F2%5C-0.1+=+493.926218353009

Quadratic expression -0.1x%5E2%2B50x%2B-300 can be factored:
-0.1x%5E2%2B50x%2B-300+=+-0.1%28x-6.07378164699064%29%2A%28x-493.926218353009%29
Again, the answer is: 6.07378164699064, 493.926218353009. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.1%2Ax%5E2%2B50%2Ax%2B-300+%29