document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952637>Question 952637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has a length of 31 feet less than 6 times its width.  If the area of the rectangle is 4470 square feet, find the length 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 #581761 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=581761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> W=width; L=length=6W-31ft;<BR>\n" );
document.write( "A=L*W<BR>\n" );
document.write( "4470sqft=(6W-31ft)(W)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4470ft%5E2=6W%5E2-31W ALIGN=MIDDLE  ALT=\"4470ft%5E2=6W%5E2-31W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=6W%5E2-31W-4470ft%5E2 ALIGN=MIDDLE  ALT=\"0=6W%5E2-31W-4470ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=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=6W%5E2%2B-31W%2B-4470+=+0 ALIGN=MIDDLE  ALT=\"6W%5E2%2B-31W%2B-4470+=+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=%28-31%29%5E2-4%2A6%2A-4470=108241 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-31%29%5E2-4%2A6%2A-4470=108241\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=108241 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--31%2B-sqrt%28+108241+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--31%2B-sqrt%28+108241+%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-%28-31%29%2Bsqrt%28+108241+%29%29%2F2%5C6+=+30 ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%28-%28-31%29%2Bsqrt%28+108241+%29%29%2F2%5C6+=+30\"   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-%28-31%29-sqrt%28+108241+%29%29%2F2%5C6+=+-24.8333333333333 ALIGN=MIDDLE  ALT=\"W%5B2%5D+=+%28-%28-31%29-sqrt%28+108241+%29%29%2F2%5C6+=+-24.8333333333333\"   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=6W%5E2%2B-31W%2B-4470 ALIGN=MIDDLE  ALT=\"6W%5E2%2B-31W%2B-4470\"   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=6W%5E2%2B-31W%2B-4470+=+6%28W-30%29%2A%28W--24.8333333333333%29 ALIGN=MIDDLE  ALT=\"6W%5E2%2B-31W%2B-4470+=+6%28W-30%29%2A%28W--24.8333333333333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 30, -24.8333333333333.\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+6%2Ax%5E2%2B-31%2Ax%2B-4470+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B-31%2Ax%2B-4470+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "The width is 30 feet.<BR>\n" );
document.write( "L=6W-31ft+6(30ft)-31ft=180ft-31ft=149ft ANSWER: The length is 149 feet<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "A=L*W<BR>\n" );
document.write( "4470sqft=149ft*30ft<BR>\n" );
document.write( "4470sqft=4470sqft </SPAN>\n" );
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