document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=936218>Question 936218</A>: <I><SPAN STYLE=\"word-break: break-all;\"> mr.jackson has a rectangular shaped garden where the length was 4 less than twice the width. if the area of the garden is 420 square feet, find the dimensions of the garden to the nearest hundredth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569657 by </B><A HREF=/tutors/aboutme.mpl?userid=srinivas.g><B>srinivas.g(540)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=srinivas.g><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=srinivas.g><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=569657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let width be x feet<BR>\n" );
document.write( " length was 4 less than twice the width<BR>\n" );
document.write( "  length  = 2*x-4<BR>\n" );
document.write( "  area  = width x length<BR>\n" );
document.write( "  420 = x* (2x-4)<BR>\n" );
document.write( "   420 = x*2x-x*4<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+420+=2x%5E2-4x ALIGN=MIDDLE  ALT=\"+420+=2x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    move 420 to the right<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2x%5E2-4x-420 ALIGN=MIDDLE  ALT=\"0+=+2x%5E2-4x-420\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=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=2x%5E2%2B-4x%2B-420+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-4x%2B-420+=+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=%28-4%29%5E2-4%2A2%2A-420=3376 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4%29%5E2-4%2A2%2A-420=3376\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3376 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--4%2B-sqrt%28+3376+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--4%2B-sqrt%28+3376+%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-%28-4%29%2Bsqrt%28+3376+%29%29%2F2%5C2+=+15.5258390463339 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+3376+%29%29%2F2%5C2+=+15.5258390463339\"   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-%28-4%29-sqrt%28+3376+%29%29%2F2%5C2+=+-13.5258390463339 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-4%29-sqrt%28+3376+%29%29%2F2%5C2+=+-13.5258390463339\"   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=2x%5E2%2B-4x%2B-420 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-4x%2B-420\"   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=2x%5E2%2B-4x%2B-420+=+2%28x-15.5258390463339%29%2A%28x--13.5258390463339%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-4x%2B-420+=+2%28x-15.5258390463339%29%2A%28x--13.5258390463339%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 15.5258390463339, -13.5258390463339.\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+2%2Ax%5E2%2B-4%2Ax%2B-420+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-4%2Ax%2B-420+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " x= 15.53 , -13.53<BR>\n" );
document.write( " but x cannot be negative<BR>\n" );
document.write( " hence  width (w) = 15.53  feet<BR>\n" );
document.write( " length (l) = 2*15.53-4<BR>\n" );
document.write( "            = 31.06-4<BR>\n" );
document.write( "             = 27.06 feet<BR>\n" );
document.write( "length  = 27.06 feet & width  = 15.53 feet </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );