document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437160>Question 437160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular storage area is 8.0 meter longer than it is wide. If the area is 28m^2, what are its dimensions? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302373 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=302373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area = Length * Width<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We're told <BR>\n" );
document.write( "A = 28<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We're also told the length is 8 meters greater than width.<BR>\n" );
document.write( "L = W+8<BR>\n" );
document.write( ".<BR>\n" );
document.write( "L * W = A<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substituting:<BR>\n" );
document.write( "(W+8) * W = 28<BR>\n" );
document.write( "W^2 + 8W = 28<BR>\n" );
document.write( "Subtract 28 from both sides<BR>\n" );
document.write( "W^2 + 8W - 28 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This does not factor easily, so use the quadratic equation.<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%2B8W%2B-28+=+0 ALIGN=MIDDLE  ALT=\"1W%5E2%2B8W%2B-28+=+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=%288%29%5E2-4%2A1%2A-28=176 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%288%29%5E2-4%2A1%2A-28=176\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=176 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+=+%28-8%2B-sqrt%28+176+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-8%2B-sqrt%28+176+%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-%288%29%2Bsqrt%28+176+%29%29%2F2%5C1+=+2.6332495807108 ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%28-%288%29%2Bsqrt%28+176+%29%29%2F2%5C1+=+2.6332495807108\"   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-%288%29-sqrt%28+176+%29%29%2F2%5C1+=+-10.6332495807108 ALIGN=MIDDLE  ALT=\"W%5B2%5D+=+%28-%288%29-sqrt%28+176+%29%29%2F2%5C1+=+-10.6332495807108\"   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%2B8W%2B-28 ALIGN=MIDDLE  ALT=\"1W%5E2%2B8W%2B-28\"   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%2B8W%2B-28+=+1%28W-2.6332495807108%29%2A%28W--10.6332495807108%29 ALIGN=MIDDLE  ALT=\"1W%5E2%2B8W%2B-28+=+1%28W-2.6332495807108%29%2A%28W--10.6332495807108%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.6332495807108, -10.6332495807108.\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%2B8%2Ax%2B-28+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-28+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( "A negative value for W does not make sense, so we choose W = 2.633.<BR>\n" );
document.write( "L = W + 8 = 10.633.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Checking.<BR>\n" );
document.write( "10.633*2.633=27.9966 or about 28.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );