SOLUTION: The profit, P, of a video company in thousands of dollars, is given by P = -5x^2 + 550x -5000, where x is the amount spent on advertising in thousands of dollars. Determ

Algebra ->  Equations -> SOLUTION: The profit, P, of a video company in thousands of dollars, is given by P = -5x^2 + 550x -5000, where x is the amount spent on advertising in thousands of dollars. Determ      Log On


   

Question 763065: The profit, P, of a video company in thousands of dollars, is given by
P = -5x^2 + 550x -5000, where x is the amount spent on advertising in thousands of dollars.

Determine the amount spent on advertising that will result in a profit of $0.In other words, you will determine the amount that must be spent on advertising in order for the company to “ break even.”
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
P = -5*x^2 + 550*x - 5000
When P = 0
-5*x^2 + 550*x - 5000 = 0
Dividing by -5,
x^2 - 110x + 1000 = 0
(x - 100)*(x - 10) = 0
x = 100 or 10
Profit is 0 when the spend is 100000 dollars or 10000 dollars.
See the quadratic solution below as well
:)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-110x%2B1000+=+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=%28-110%29%5E2-4%2A1%2A1000=8100.

Discriminant d=8100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--110%2B-sqrt%28+8100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-110%29%2Bsqrt%28+8100+%29%29%2F2%5C1+=+100
x%5B2%5D+=+%28-%28-110%29-sqrt%28+8100+%29%29%2F2%5C1+=+10

Quadratic expression 1x%5E2%2B-110x%2B1000 can be factored:
1x%5E2%2B-110x%2B1000+=+1%28x-100%29%2A%28x-10%29
Again, the answer is: 100, 10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-110%2Ax%2B1000+%29