document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=580348>Question 580348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been working on this math problem for the past 2 hours and is having a difficult time with it. Can anyone please help me.\r<BR>\n" );
document.write( "\n" );
document.write( "p(x)= -.1x^2+50x-300, where x is the number of items sold, x>0.\r<BR>\n" );
document.write( "\n" );
document.write( "Please and 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 #371213 by </B><A HREF=/tutors/aboutme.mpl?userid=dfrazzetto><B>dfrazzetto(283)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dfrazzetto><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=dfrazzetto><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=371213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p(x)= -.1x^2+50x-300, where x is the number of items sold, x>0.\r<BR>\n" );
document.write( "\n" );
document.write( "what do you want to know?  P given a certain value of x? or if P(x) = some value, find x??\r<BR>\n" );
document.write( "\n" );
document.write( "You haven't asked a question yet.\r<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=-0.1x%5E2%2B50x%2B-300+=+0 ALIGN=MIDDLE  ALT=\"-0.1x%5E2%2B50x%2B-300+=+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=%2850%29%5E2-4%2A-0.1%2A-300=2380 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2850%29%5E2-4%2A-0.1%2A-300=2380\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2380 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+=+%28-50%2B-sqrt%28+2380+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-50%2B-sqrt%28+2380+%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-%2850%29%2Bsqrt%28+2380+%29%29%2F2%5C-0.1+=+6.07378164699064 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2850%29%2Bsqrt%28+2380+%29%29%2F2%5C-0.1+=+6.07378164699064\"   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-%2850%29-sqrt%28+2380+%29%29%2F2%5C-0.1+=+493.926218353009 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2850%29-sqrt%28+2380+%29%29%2F2%5C-0.1+=+493.926218353009\"   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=-0.1x%5E2%2B50x%2B-300 ALIGN=MIDDLE  ALT=\"-0.1x%5E2%2B50x%2B-300\"   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=-0.1x%5E2%2B50x%2B-300+=+-0.1%28x-6.07378164699064%29%2A%28x-493.926218353009%29 ALIGN=MIDDLE  ALT=\"-0.1x%5E2%2B50x%2B-300+=+-0.1%28x-6.07378164699064%29%2A%28x-493.926218353009%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.07378164699064, 493.926218353009.\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+-0.1%2Ax%5E2%2B50%2Ax%2B-300+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.1%2Ax%5E2%2B50%2Ax%2B-300+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );