document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956703>Question 956703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangular door is 20.77 square feet. The width of the door is 3.6 feet more than its length. Find the length and width of the door. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584513 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=584513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> L=length; W=width=L+3.6ft; A=area=20.77 sq ft<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW=A ALIGN=MIDDLE  ALT=\"LW=A\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for W<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%28L%2B3.6ft%29=20.77ft%5E2 ALIGN=MIDDLE  ALT=\"L%28L%2B3.6ft%29=20.77ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2B3.6Lft=20.77ft%5E2 ALIGN=MIDDLE  ALT=\"L%5E2%2B3.6Lft=20.77ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 20.77 sq ft from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2B3.6ftL-20.77ft%5E2=0 ALIGN=MIDDLE  ALT=\"L%5E2%2B3.6ftL-20.77ft%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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%2B3.6L%2B-20.77+=+0 ALIGN=MIDDLE  ALT=\"1L%5E2%2B3.6L%2B-20.77+=+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=%283.6%29%5E2-4%2A1%2A-20.77=96.04 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283.6%29%5E2-4%2A1%2A-20.77=96.04\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=96.04 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+=+%28-3.6%2B-sqrt%28+96.04+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3.6%2B-sqrt%28+96.04+%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-%283.6%29%2Bsqrt%28+96.04+%29%29%2F2%5C1+=+3.1 ALIGN=MIDDLE  ALT=\"L%5B1%5D+=+%28-%283.6%29%2Bsqrt%28+96.04+%29%29%2F2%5C1+=+3.1\"   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-%283.6%29-sqrt%28+96.04+%29%29%2F2%5C1+=+-6.7 ALIGN=MIDDLE  ALT=\"L%5B2%5D+=+%28-%283.6%29-sqrt%28+96.04+%29%29%2F2%5C1+=+-6.7\"   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%2B3.6L%2B-20.77 ALIGN=MIDDLE  ALT=\"1L%5E2%2B3.6L%2B-20.77\"   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%2B3.6L%2B-20.77+=+1%28L-3.1%29%2A%28L--6.7%29 ALIGN=MIDDLE  ALT=\"1L%5E2%2B3.6L%2B-20.77+=+1%28L-3.1%29%2A%28L--6.7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.1, -6.7.\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%2B3.6%2Ax%2B-20.77+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3.6%2Ax%2B-20.77+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "ANSWER 1: The length is 3.1 feet.<BR>\n" );
document.write( "W=L+3.6ft=3.1ft+3.6ft=6.7ft<BR>\n" );
document.write( "ANSWER 2: The width is 6.7 feet.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LW=A ALIGN=MIDDLE  ALT=\"LW=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283.1ft%29%286.7ft%29=20.77ft%5E2 ALIGN=MIDDLE  ALT=\"%283.1ft%29%286.7ft%29=20.77ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.77ft%5E2=20.77ft%5E2 ALIGN=MIDDLE  ALT=\"20.77ft%5E2=20.77ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );