document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=949571>Question 949571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The length of a rectangle is 3 feet less than twice its width and area of rectangle is 27 ft2.  Find the dimension\r<BR>\n" );
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document.write( "Lenth=\r<BR>\n" );
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document.write( "Width= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #579740 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=579740\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> W=width; L=length=2W-3 ft; A=L*W=27 sq ft<BR>\n" );
document.write( "A=L*W Substitute for L<BR>\n" );
document.write( "27 sq ft=(2W-3)(W)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27+sq+ft=2W%5E2-3W ALIGN=MIDDLE  ALT=\"27+sq+ft=2W%5E2-3W\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 27 from each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2W%5E2-3W-27 ALIGN=MIDDLE  ALT=\"0=2W%5E2-3W-27\"   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=2W%5E2%2B-3W%2B-27+=+0 ALIGN=MIDDLE  ALT=\"2W%5E2%2B-3W%2B-27+=+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=%28-3%29%5E2-4%2A2%2A-27=225 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-27=225\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=225 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%2B-sqrt%28+225+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--3%2B-sqrt%28+225+%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-%28-3%29%2Bsqrt%28+225+%29%29%2F2%5C2+=+4.5 ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+225+%29%29%2F2%5C2+=+4.5\"   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-%28-3%29-sqrt%28+225+%29%29%2F2%5C2+=+-3 ALIGN=MIDDLE  ALT=\"W%5B2%5D+=+%28-%28-3%29-sqrt%28+225+%29%29%2F2%5C2+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2W%5E2%2B-3W%2B-27 ALIGN=MIDDLE  ALT=\"2W%5E2%2B-3W%2B-27\"   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=2W%5E2%2B-3W%2B-27+=+2%28W-4.5%29%2A%28W--3%29 ALIGN=MIDDLE  ALT=\"2W%5E2%2B-3W%2B-27+=+2%28W-4.5%29%2A%28W--3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.5, -3.\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-3%2Ax%2B-27+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-27+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "ANSWER 1: W=4.5 ft  The width is 4.5 feet.<BR>\n" );
document.write( "L=2W-3 ft=2(4.5)-3 ft=9 feet-3 feet=6 feet ANSWER 2: The length is 6 feet.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "A=L*W<BR>\n" );
document.write( "27 sq ft=(6 ft)(4.5 ft)<BR>\n" );
document.write( "27 sq ft=27 sq ft </SPAN>\n" );
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