document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992571>Question 992571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cynthia Besch wants to buy a rug for a room that is 18 feet wide and 19 feet long. She wants to leave a uniform strip around the rug. She can afford 272 square feet of carpeting. What dimensions should the rug have?\r<BR>\n" );
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document.write( "272+(19-2x)(18+2x)<BR>\n" );
document.write( "1, 35/2\r<BR>\n" );
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document.write( "But, what are the dimensions in feet? How do I convert? Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612157 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=612157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the width of the strip be x<BR>\n" );
document.write( "The rug will have square footage of (18-2x)*(19-2x)<BR>\n" );
document.write( "you are told she wants a rug that is 272 sq ft\r<BR>\n" );
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document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=272+=+%2818-2x%29%2A%2819-2x%29 ALIGN=MIDDLE  ALT=\"272+=+%2818-2x%29%2A%2819-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=272+=+342+-+36x+-+38x+%2B+4x%5E2 ALIGN=MIDDLE  ALT=\"272+=+342+-+36x+-+38x+%2B+4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+4x%5E2+-+74x+%2B+70 ALIGN=MIDDLE  ALT=\"0+=+4x%5E2+-+74x+%2B+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\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=4x%5E2%2B-74x%2B70+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-74x%2B70+=+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=%28-74%29%5E2-4%2A4%2A70=4356 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-74%29%5E2-4%2A4%2A70=4356\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4356 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--74%2B-sqrt%28+4356+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--74%2B-sqrt%28+4356+%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-%28-74%29%2Bsqrt%28+4356+%29%29%2F2%5C4+=+17.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-74%29%2Bsqrt%28+4356+%29%29%2F2%5C4+=+17.5\"   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-%28-74%29-sqrt%28+4356+%29%29%2F2%5C4+=+1 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-74%29-sqrt%28+4356+%29%29%2F2%5C4+=+1\"   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=4x%5E2%2B-74x%2B70 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-74x%2B70\"   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=4x%5E2%2B-74x%2B70+=+4%28x-17.5%29%2A%28x-1%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B-74x%2B70+=+4%28x-17.5%29%2A%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 17.5, 1.\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+4%2Ax%5E2%2B-74%2Ax%2B70+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-74%2Ax%2B70+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "so the strip will be 1 ft wide<BR>\n" );
document.write( "That makes the rug (18-2) by (19-2) feet<BR>\n" );
document.write( "16 feet by 17 feet </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );