document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462147>Question 462147</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the cost C, in dollars, of producing x chairs in a factory is given by the following equation:\r<BR>\n" );
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document.write( "C = 2x2 – 40x + 2400\r<BR>\n" );
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document.write( "How many chairs can be produced for $4650?\r<BR>\n" );
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document.write( "Your Solution\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316872 by </B><A HREF=/tutors/aboutme.mpl?userid=graphmatics><B>graphmatics(170)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=graphmatics><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=graphmatics><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let us first replace the C in the equation C = 2x^2 – 40*x + 2400 by the amount $4650. So we get<BR>\n" );
document.write( "4650 = 2*x^2 – 40*x + 2400 <BR>\n" );
document.write( "0 = 2*x^2 - 40*x + 2400 - 4650<BR>\n" );
document.write( "0 = 2*x^2 - 40*x - 2250<BR>\n" );
document.write( "Let's divide out the 2 and get<BR>\n" );
document.write( "0 = x^2 - 20*x - 1125<BR>\n" );
document.write( "x^2 - 20*x - 1125 = 0<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=quadratic.solver>SOLVE quadratic equation with variable</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=1x%5E2%2B-20x%2B-1125+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-20x%2B-1125+=+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" );
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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" );
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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=%28-20%29%5E2-4%2A1%2A-1125=4900 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-20%29%5E2-4%2A1%2A-1125=4900\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "  Discriminant d=4900 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+4900+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--20%2B-sqrt%28+4900+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+4900+%29%29%2F2%5C1+=+45 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+4900+%29%29%2F2%5C1+=+45\"   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-%28-20%29-sqrt%28+4900+%29%29%2F2%5C1+=+-25 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-20%29-sqrt%28+4900+%29%29%2F2%5C1+=+-25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-20x%2B-1125 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-20x%2B-1125\"   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=1x%5E2%2B-20x%2B-1125+=+1%28x-45%29%2A%28x--25%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-20x%2B-1125+=+1%28x-45%29%2A%28x--25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 45, -25.\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+1%2Ax%5E2%2B-20%2Ax%2B-1125+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-20%2Ax%2B-1125+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So x = 45 is how many chairs can be produced for $4650<BR>\n" );
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