SOLUTION: I am trying to find the breakeven point for this problem: A company that manufacturers and sells rubber chickens has determined that hte profit earned from selling x thousand ch

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Question 943355: I am trying to find the breakeven point for this problem:
A company that manufacturers and sells rubber chickens has determined that hte profit earned from selling x thousand chickens in given by
P(x) = -0.8x^2 + 16.2x - 10
where 0 <= x <= 22

I have everything with the graph all done, I just need help on how to fund the breakeven point.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
P%28x%29+=+-0.8x%5E2+%2B+16.2x+-+10
where 0+%3C=+x+%3C=+22+
to find the breakeven point for this problem, set P%28x%29+=+0 and solve for x
0=+-0.8x%5E2+%2B+16.2x+-+10 ...multiply all terms by 10 to get rid of decimals
0=+-8x%5E2+%2B+162x+-+100
0=+-2%284x%5E2+-+81x+%2B+50%29 this product will be equal to 0 if
0=+%284x%5E2+-+81x+%2B+50%29 ...use quadratic formula to find x

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-81%29+%2B-+sqrt%28+%28-81%29+%5E2-4%2A4%2A50+%29%29%2F%282%2A4%29+

x+=+%2881+%2B-+sqrt%28+6561-800+%29%29%2F8+

x+=+%2881+%2B-+sqrt%28+5761+%29%29%2F8+

x+=+%2881+%2B-+75.9%29%2F8+
solutions:
x+=+%2881+%2B+75.9%29%2F8+
x+=+156.9%2F8+
highlight%28x+=19.6%29
or
x+=+%2881+-+75.9%29%2F8+
x+=+5.1%2F8+
highlight%28x+=0.6%29

so, both solutions satisfy given condition 0+%3C=+x+%3C=+22+
0+%3C=+19.6+%3C=+22+
0+%3C=+0.6+%3C=+22+

+graph%28+600%2C+600%2C+-10%2C+35%2C+-25%2C+75%2C+-0.8x%5E2+%2B+16.2x+-+10%29+