document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=943355>Question 943355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to find the breakeven point for this problem:\r<BR>\n" );
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document.write( "A company that manufacturers and sells rubber chickens has determined that hte profit earned from selling x thousand chickens in given by<BR>\n" );
document.write( "                       P(x) = -0.8x^2 + 16.2x - 10<BR>\n" );
document.write( "where 0 <= x <= 22\r<BR>\n" );
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document.write( "I have everything with the graph all done, I just need help on how to fund the breakeven point. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #575158 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=575158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+-0.8x%5E2+%2B+16.2x+-+10 ALIGN=MIDDLE  ALT=\"P%28x%29+=+-0.8x%5E2+%2B+16.2x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+22+ ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "to find the breakeven point for this problem, set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+0 ALIGN=MIDDLE  ALT=\"P%28x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-0.8x%5E2+%2B+16.2x+-+10 ALIGN=MIDDLE  ALT=\"0=+-0.8x%5E2+%2B+16.2x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...multiply all terms by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get rid of decimals\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-8x%5E2+%2B+162x+-+100 ALIGN=MIDDLE  ALT=\"0=+-8x%5E2+%2B+162x+-+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+-2%284x%5E2+-+81x+%2B+50%29 ALIGN=MIDDLE  ALT=\"0=+-2%284x%5E2+-+81x+%2B+50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > this product will be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > if\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+%284x%5E2+-+81x+%2B+50%29 ALIGN=MIDDLE  ALT=\"0=+%284x%5E2+-+81x+%2B+50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...use quadratic formula to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-81%29+%2B-+sqrt%28+%28-81%29+%5E2-4%2A4%2A50+%29%29%2F%282%2A4%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-81%29+%2B-+sqrt%28+%28-81%29+%5E2-4%2A4%2A50+%29%29%2F%282%2A4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2881+%2B-+sqrt%28+6561-800+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2881+%2B-+sqrt%28+6561-800+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2881+%2B-+sqrt%28+5761+%29%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2881+%2B-+sqrt%28+5761+%29%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2881+%2B-+75.9%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2881+%2B-+75.9%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2881+%2B+75.9%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2881+%2B+75.9%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+156.9%2F8+ ALIGN=MIDDLE  ALT=\"x+=+156.9%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=19.6%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=19.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2881+-+75.9%29%2F8+ ALIGN=MIDDLE  ALT=\"x+=+%2881+-+75.9%29%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5.1%2F8+ ALIGN=MIDDLE  ALT=\"x+=+5.1%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=0.6%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=0.6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,  both solutions satisfy given condition <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+x+%3C=+22+ ALIGN=MIDDLE  ALT=\"0+%3C=+x+%3C=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+19.6+%3C=+22+ ALIGN=MIDDLE  ALT=\"0+%3C=+19.6+%3C=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+%3C=+0.6+%3C=+22+ ALIGN=MIDDLE  ALT=\"0+%3C=+0.6+%3C=+22+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+35%2C+-25%2C+75%2C+-0.8x%5E2+%2B+16.2x+-+10%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+35%2C+-25%2C+75%2C+-0.8x%5E2+%2B+16.2x+-+10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );