document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=240171>Question 240171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine how long the cannon ball was in the air.<BR>\n" );
document.write( "using h=-5t(squared)+ 40t+ 3<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 #176055 by </B><A HREF=/tutors/aboutme.mpl?userid=philline_palana><B>philline_palana(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=philline_palana><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=philline_palana><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\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=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5t%5E2%2B40t%2B3+=+0 ALIGN=MIDDLE  ALT=\"-5t%5E2%2B40t%2B3+=+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=t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"t%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=%2840%29%5E2-4%2A-5%2A3=1660 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2840%29%5E2-4%2A-5%2A3=1660\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1660 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+=+%28-40%2B-sqrt%28+1660+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-40%2B-sqrt%28+1660+%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=t%5B1%5D+=+%28-%2840%29%2Bsqrt%28+1660+%29%29%2F2%5C-5+=+-0.0743097574926722 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2840%29%2Bsqrt%28+1660+%29%29%2F2%5C-5+=+-0.0743097574926722\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+%28-%2840%29-sqrt%28+1660+%29%29%2F2%5C-5+=+8.07430975749267 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2840%29-sqrt%28+1660+%29%29%2F2%5C-5+=+8.07430975749267\"   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=-5t%5E2%2B40t%2B3 ALIGN=MIDDLE  ALT=\"-5t%5E2%2B40t%2B3\"   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=-5t%5E2%2B40t%2B3+=+-5%28t--0.0743097574926722%29%2A%28t-8.07430975749267%29 ALIGN=MIDDLE  ALT=\"-5t%5E2%2B40t%2B3+=+-5%28t--0.0743097574926722%29%2A%28t-8.07430975749267%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0743097574926722, 8.07430975749267.\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+-5%2Ax%5E2%2B40%2Ax%2B3+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B40%2Ax%2B3+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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