document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946706>Question 946706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The width of a rectangle is 5 less than twice its length. If the area of the rectangle is 122 square centimeters, what is the length of the diagonal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577557 by </B><A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><B>amarjeeth123(574)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><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=577557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the length of the rectangle be x.<BR>\n" );
document.write( "Width of the rectangle=2x-5<BR>\n" );
document.write( "Area of the rectangle=x(2x-5)<BR>\n" );
document.write( "x(2x-5)=122<BR>\n" );
document.write( "2x^2-5x-122=0<BR>\n" );
document.write( "x^2-2.5x-61=0<BR>\n" );
document.write( "<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=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-2.5x%2B-61+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2.5x%2B-61+=+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=%28-2.5%29%5E2-4%2A1%2A-61=250.25 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-2.5%29%5E2-4%2A1%2A-61=250.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=250.25 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--2.5%2B-sqrt%28+250.25+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--2.5%2B-sqrt%28+250.25+%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-%28-2.5%29%2Bsqrt%28+250.25+%29%29%2F2%5C1+=+9.15964600977819 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-2.5%29%2Bsqrt%28+250.25+%29%29%2F2%5C1+=+9.15964600977819\"   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-%28-2.5%29-sqrt%28+250.25+%29%29%2F2%5C1+=+-6.65964600977819 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-2.5%29-sqrt%28+250.25+%29%29%2F2%5C1+=+-6.65964600977819\"   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=1x%5E2%2B-2.5x%2B-61 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2.5x%2B-61\"   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-2.5x%2B-61+=+1%28x-9.15964600977819%29%2A%28x--6.65964600977819%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-2.5x%2B-61+=+1%28x-9.15964600977819%29%2A%28x--6.65964600977819%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 9.15964600977819, -6.65964600977819.\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-2.5%2Ax%2B-61+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2.5%2Ax%2B-61+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "x=9.16<BR>\n" );
document.write( "2x-5=13.32<BR>\n" );
document.write( "Length of the diagonal=16.16 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );