document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=991021>Question 991021</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 6 cm more than the width. The area is 11 cm^2. Find the  length and width. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #610944 by </B><A HREF=/tutors/aboutme.mpl?userid=Timnewman><B>Timnewman(323)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Timnewman><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=Timnewman><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=610944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi dear,<BR>\n" );
document.write( "let L=lenght,<BR>\n" );
document.write( "w=width<BR>\n" );
document.write( "Then,from your question,<BR>\n" );
document.write( "L=w+6-----(1)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "L*w=11----(2)<BR>\n" );
document.write( "Put 1 in 2,<BR>\n" );
document.write( "(w+6)w=11<BR>\n" );
document.write( "w²+6w-11=0<BR>\n" );
document.write( "Solve the resulting quadratic equation as follows:<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=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B6w%2B-11+=+0 ALIGN=MIDDLE  ALT=\"1w%5E2%2B6w%2B-11+=+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=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%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=%286%29%5E2-4%2A1%2A-11=80 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%286%29%5E2-4%2A1%2A-11=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=80 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+=+%28-6%2B-sqrt%28+80+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-6%2B-sqrt%28+80+%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=w%5B1%5D+=+%28-%286%29%2Bsqrt%28+80+%29%29%2F2%5C1+=+1.47213595499958 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%286%29%2Bsqrt%28+80+%29%29%2F2%5C1+=+1.47213595499958\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%286%29-sqrt%28+80+%29%29%2F2%5C1+=+-7.47213595499958 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%286%29-sqrt%28+80+%29%29%2F2%5C1+=+-7.47213595499958\"   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=1w%5E2%2B6w%2B-11 ALIGN=MIDDLE  ALT=\"1w%5E2%2B6w%2B-11\"   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=1w%5E2%2B6w%2B-11+=+1%28w-1.47213595499958%29%2A%28w--7.47213595499958%29 ALIGN=MIDDLE  ALT=\"1w%5E2%2B6w%2B-11+=+1%28w-1.47213595499958%29%2A%28w--7.47213595499958%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.47213595499958, -7.47213595499958.\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%2B6%2Ax%2B-11+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-11+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Then w=1.5cm,w=-7.3cm<BR>\n" );
document.write( "When w=1.9,<BR>\n" );
document.write( "L=1.9+6<BR>\n" );
document.write( "L=7.9cm<BR>\n" );
document.write( "when w=-7.3,<BR>\n" );
document.write( "L=-7.3+6<BR>\n" );
document.write( "L=-1.3cm </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );