document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=747328>Question 747328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's <BR>\n" );
document.write( "The length of a rectangle is 3 feet less than twice the width. The area is 44 square feet. Find the length and the width? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #454845 by </B><A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><B>timvanswearingen(106)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=timvanswearingen><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=timvanswearingen><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=454845\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w be the width.  <BR>\n" );
document.write( "Then the length can be represented by 2w-3 (3 less than twice the width)\r<BR>\n" );
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document.write( "The area of a rectangle is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=l%2Aw ALIGN=MIDDLE  ALT=\"A=l%2Aw\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, plug in for A, l and w.\r<BR>\n" );
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document.write( "{{44=(2w-3)(w)}}}\r<BR>\n" );
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document.write( "Distribute,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=44=2w%5E2-3w ALIGN=MIDDLE  ALT=\"44=2w%5E2-3w\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract 44 from both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=2w%5E2-3w-44 ALIGN=MIDDLE  ALT=\"0=2w%5E2-3w-44\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since I'm not sure how to show you the regrouping hourglass method on here, I've used the quadratic solver from this site to get to the solution for you.  You can always use the quadratic formula when solving quadratics.  See below the graph for the final explanation and answer.\r<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=2x%5E2%2B-3x%2B-44+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-3x%2B-44+=+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=%28-3%29%5E2-4%2A2%2A-44=361 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-44=361\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=361 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+361+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--3%2B-sqrt%28+361+%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-%28-3%29%2Bsqrt%28+361+%29%29%2F2%5C2+=+5.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+361+%29%29%2F2%5C2+=+5.5\"   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-%28-3%29-sqrt%28+361+%29%29%2F2%5C2+=+-4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-3%29-sqrt%28+361+%29%29%2F2%5C2+=+-4\"   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-3x%2B-44 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-3x%2B-44\"   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-3x%2B-44+=+2%28x-5.5%29%2A%28x--4%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-3x%2B-44+=+2%28x-5.5%29%2A%28x--4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 5.5, -4.\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-44+%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-44+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Since the width cannot be a negative number, you can throw out the w=-4 solution.\r<BR>\n" );
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document.write( "Thus, the width is 5.5 feet.  \r<BR>\n" );
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document.write( "The length was 3 feet less than twice the width.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=2w-3 ALIGN=MIDDLE  ALT=\"l=2w-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Plug in 5.5 for w:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=2%285.5%29-3 ALIGN=MIDDLE  ALT=\"l=2%285.5%29-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Distribute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=11-3 ALIGN=MIDDLE  ALT=\"l=11-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Simplify:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=8 ALIGN=MIDDLE  ALT=\"l=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, you have both.  l= 8ft and w= 5.5ft\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );