document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184616>Question 184616</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534490247/algebrahomeworkh>Elem. Algebra & Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of cardboaard is 2 units longer than it is wide.  From each of its corners a square piece 2 units on a side is cut out.  The flaps are then turned up to form an open box that has a volume of 70 cubic units.  Find the length and width of the original piece of cardboard.\r<BR>\n" );
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document.write( "box volume = length x width x height<BR>\n" );
document.write( "volume = 70<BR>\n" );
document.write( "width = w<BR>\n" );
document.write( "length = 2w (2 times the width)<BR>\n" );
document.write( "height = 2<BR>\n" );
document.write( "box volume would be 70=(x)(2w)(2)???<BR>\n" );
document.write( "this gives me 70=4w^2??? this seems very difficult to work with, can you help me figure this problem out? Thank you.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138621 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=138621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You need to re-read your problem.  The problem says that the length is 2 units longer than the width, not 2 times the width.  Furthermore, the width of the box formed is 4 inches less than the original width of the cardboard, and the length of the box formed is 4 inches less than the original length of the cardboard because of the 2 inch squares cut out of the corners before the box was folded.  So width is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w - 4\">, length is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large w + 2 - 4 = w - 2\">, and height is 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  V = lwh\">\r<BR>\n" );
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document.write( "So:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  2(w - 4)(w - 2) = 70 \ \ \Rightarrow\ \ 2w^2 - 12w + 16 - 70 = 0 \ \ \Rightarrow\ \ w^2 - 6w - 27 = 0\">\r<BR>\n" );
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document.write( "Note: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -9 \times 3 = -27\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large - 9 + 3 = -6\"> so this factors neatly.  One of your roots will be negative.  Discard this extraneous root because it would be absurd to have a negative measure of length.  The positive root is your width of the original cardboard and the length is two inches longer.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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