Pre-Calculus

The profit in dollars in producing x items of some commodity is given by the equation P=−11x2+346.5x−2612.5.
How many items should be produced to break even?(If there are two break-even points, then enter the smaller value of x. Your solution may not be an integer. Use your calculator for irrational square roots.)

I know that P(x)=revenue - cost, but I don't know how to set revenue and cost equal to each other to find break-even if they are already combined in −11x2+346.5x−2612.5...

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  1. The function is P=−11x^2+346.5x−2612.5

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  2. break-even is where profit=0.

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  3. I think your equation already contains revenue and cost, since it is labeled as "profit"
    I interpret "break-even" point as having no loss or profit, or , P = 0
    so we want the roots of
    -11x^2 + 346.5x - 2612.5

    x = (-346.5 ± √(5112.25)/-22
    = 12.5 or 19

    Wolfram confirms my answers
    http://www.wolframalpha.com/input/?i=−11x%5E2%2B346.5x−2612.5%3D0+

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  4. Oh yeah I forgot it meant that P = 0 thanks

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