document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=330594>Question 330594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the width of a rectangle is 5cm less than half its length. Its area is 72 cm squared. What is the length and width of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #236993 by </B><A HREF=/tutors/aboutme.mpl?userid=JBarnum><B>JBarnum(2146)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JBarnum><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=JBarnum><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=236993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a=lw  know your formulas<BR>\n" );
document.write( "a=72<BR>\n" );
document.write( "w=(l/2)-5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72=l%28%28l%2F2%29-5%29 ALIGN=MIDDLE  ALT=\"72=l%28%28l%2F2%29-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72=%28l%5E2%2F2%29-5l ALIGN=MIDDLE  ALT=\"72=%28l%5E2%2F2%29-5l\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144=l%5E2-10l ALIGN=MIDDLE  ALT=\"144=l%5E2-10l\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=l%5E2-10l-144 ALIGN=MIDDLE  ALT=\"0=l%5E2-10l-144\"   DISABLED_style= \"max-width:90%; height:auto;\" > view below for quadratic explaination<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=18 ALIGN=MIDDLE  ALT=\"l=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "72/18=w<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=4 ALIGN=MIDDLE  ALT=\"w=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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=al%5E2%2Bbl%2Bc=0 ALIGN=MIDDLE  ALT=\"al%5E2%2Bbl%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1l%5E2%2B-10l%2B-144+=+0 ALIGN=MIDDLE  ALT=\"1l%5E2%2B-10l%2B-144+=+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=l%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"l%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=%28-10%29%5E2-4%2A1%2A-144=676 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-10%29%5E2-4%2A1%2A-144=676\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=676 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--10%2B-sqrt%28+676+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--10%2B-sqrt%28+676+%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=l%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+676+%29%29%2F2%5C1+=+18 ALIGN=MIDDLE  ALT=\"l%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+676+%29%29%2F2%5C1+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l%5B2%5D+=+%28-%28-10%29-sqrt%28+676+%29%29%2F2%5C1+=+-8 ALIGN=MIDDLE  ALT=\"l%5B2%5D+=+%28-%28-10%29-sqrt%28+676+%29%29%2F2%5C1+=+-8\"   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=1l%5E2%2B-10l%2B-144 ALIGN=MIDDLE  ALT=\"1l%5E2%2B-10l%2B-144\"   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=1l%5E2%2B-10l%2B-144+=+1%28l-18%29%2A%28l--8%29 ALIGN=MIDDLE  ALT=\"1l%5E2%2B-10l%2B-144+=+1%28l-18%29%2A%28l--8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 18, -8.\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-10%2Ax%2B-144+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B-144+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );