Quadratic HELP!

[shqiptar_1029]

The profit, P, of a video company, in thousands of dollars, is given by P= -5x² + 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 amounts that must be spent on advertising in order for the company to "break even."

[niksdoon]

If we equate this to 0, it becomes a quadtratic
5x^2 - 550x + 5000 = 0

Solving this gives 2 values for x ---> (110 + 10 sqrt(101))/2, (110 - 10 sqrt(101))/2

Not sure which should be the correct one. Want to see solution from experts.

[akhp77]

-5*x*x + 550*x -5000 = 0
x*x - 110*x + 1000 = 0
(x - 100)(x-10) = 0

x = 10 or 100

Profit will vanish when amount spend on advertisement is either 10 thousand or 100 thousand Dollars.

[jnelson0612]

-5*x*x + 550*x -5000 = 0
x*x - 110*x + 1000 = 0
(x - 100)(x-10) = 0

x = 10 or 100

Profit will vanish when amount spend on advertisement is either 10 thousand or 100 thousand Dollars.

Nice work on unraveling this problem!

We need to think about what this data actually means, and don't hesitate to plug these numbers and some nearby data points to help us interpret. I deduced that profit will not occur UNTIL we spend above $10,000 on advertising, and then will disappear when we spend $100,000 or more on advertising. So our advertising needs to look like this: $10,000 < advertising < $100,000 for the company to attain a profit.