document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113087>Question 113087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the sides of a square are decreased by 2cm, the area is decreased by 36m^. What were the dimensions of the original square?\r<BR>\n" );
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document.write( "(x-6)(x+6)  Am I on the right track with this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82387 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=82387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Are you sure the area is decreased by 36 square METERS?  36 sq centimeters would make more sense.\r<BR>\n" );
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document.write( "If it actually is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36m%5E2 ALIGN=MIDDLE  ALT=\"36m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > like you say, then let x be the length of the side of the original square.\r<BR>\n" );
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document.write( "The area of the original square is then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The area of the new square would then be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36m%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-36m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But since the length of the side of the new square is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-.02m ALIGN=MIDDLE  ALT=\"x-.02m\"   DISABLED_style= \"max-width:90%; height:auto;\" >, , the area of the new square is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-.02m%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-.02m%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We can now set these two expressions for the area of the new square to be equal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36=%28x-.02%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-36=%28x-.02%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36=x%5E2-.04x%2B.0004 ALIGN=MIDDLE  ALT=\"x%5E2-36=x%5E2-.04x%2B.0004\"   DISABLED_style= \"max-width:90%; height:auto;\" >, expand the binomial using FOIL<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-36.0004=-.04x ALIGN=MIDDLE  ALT=\"-36.0004=-.04x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, collect terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=36.0004%2F.04=900.01 ALIGN=MIDDLE  ALT=\"x=36.0004%2F.04=900.01\"   DISABLED_style= \"max-width:90%; height:auto;\" >, multiply by -1 and divide by .04\r<BR>\n" );
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document.write( "The answer is 900.01 meters.\r<BR>\n" );
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document.write( "The problem set up and the equations are the same if you really meant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36cm%5E2 ALIGN=MIDDLE  ALT=\"36cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The only thing that changes are the numbers.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36=%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-36=%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36=x%5E2-4x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2-36=x%5E2-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, expand the binomial using FOIL<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40=-4x ALIGN=MIDDLE  ALT=\"-40=-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, collect terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40%2F4=10 ALIGN=MIDDLE  ALT=\"x=40%2F4=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, multiply by -1 and divide by 4\r<BR>\n" );
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document.write( "The answer is 10cm.\r<BR>\n" );
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document.write( "And to answer your question, no, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%28x%2B6%29 ALIGN=MIDDLE  ALT=\"%28x-6%29%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has nothing to do with this problem.  That is the correct factorization of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36 ALIGN=MIDDLE  ALT=\"x%5E2-36\"   DISABLED_style= \"max-width:90%; height:auto;\" > expression for the area of the new square, but as you have seen factoring this expression wasn't necessary.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "John   </SPAN>\n" );
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