document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30763>Question 30763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Publishing costs.  The cost, in dollars, of publishing x books is C(x)=40,000+20x+0.0001x^2.  How many books can be published for 250,000?<BR>\n" );
document.write( "Do I set 40,000+20x+0.0001x^2=250,000 then subtract the 250,000 so the equation =0 and then use the quadratic formula to solve?  Could someone show me the correct equation for this problem?<BR>\n" );
document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17498 by </B><A HREF=/tutors/aboutme.mpl?userid=mbarugel><B>mbarugel(146)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mbarugel><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=17498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yes, you got it right. The original equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40000%2B20x%2B0.0001x%5E2=250000+ ALIGN=MIDDLE  ALT=\"40000%2B20x%2B0.0001x%5E2=250000+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtracting 250,000, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-210000+%2B+20x+%2B0.0001x%5E2=0 ALIGN=MIDDLE  ALT=\"-210000+%2B+20x+%2B0.0001x%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And then we can solve this using the quadratic formula:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0001x%5E2%2B20x%2B-210000+=+0 ALIGN=MIDDLE  ALT=\"0.0001x%5E2%2B20x%2B-210000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2820%29%5E2-4%2A0.0001%2A-210000=484 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A0.0001%2A-210000=484\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=484 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-20%2B-sqrt%28+484+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-20%2B-sqrt%28+484+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+484+%29%29%2F2%5C0.0001+=+10000 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+484+%29%29%2F2%5C0.0001+=+10000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2820%29-sqrt%28+484+%29%29%2F2%5C0.0001+=+-210000 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2820%29-sqrt%28+484+%29%29%2F2%5C0.0001+=+-210000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0001x%5E2%2B20x%2B-210000 ALIGN=MIDDLE  ALT=\"0.0001x%5E2%2B20x%2B-210000\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.0001x%5E2%2B20x%2B-210000+=+%28x-10000%29%2A%28x--210000%29 ALIGN=MIDDLE  ALT=\"0.0001x%5E2%2B20x%2B-210000+=+%28x-10000%29%2A%28x--210000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 10000, -210000.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.0001%2Ax%5E2%2B20%2Ax%2B-210000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+0.0001%2Ax%5E2%2B20%2Ax%2B-210000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "As in any quadratic equation, we get two solutions. However, we can disregard the negative one, since it doesn't make sense in this case. The answer is that 10,000 books can be published.<BR>\n" );
document.write( "I hope this helps!<BR>\n" );
document.write( "Get more answers at <a  rel=nofollow HREF=http://www.onlinemathanswers.com>Online Math Answers.com</a>!\r<BR>\n" );
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