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"An aquarium with length x, width x-10, and height x-5 holds about 750 cubic feet of water. Find all real solutions of the equation (I wrote it) 750 = x(x-10)(x-5)."

I got the volume equation correct, right? I've tried dividing the factors of -750 by the factors of 1 (with this one theorem thingy), but I can't seem to get any real solutions. Does anyone know how to do this?

  • Precalculus -

    Your formula is correct. One root is x = 15. That is the only real solution. The other solutions are +/- sqrt(-50)

    I got the 15 by guessing. The equation
    x^3 -15x^2 +50x - 750 = 0 can be factored to give
    (x-15)(x^2 + 50) = 0

  • Precalculus -

    Ohhh I see. Thanks so much!! :D

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