document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325298>Question 325298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular lawn measuring 8m by 4m is surrounded by a flower bed of uniform width.  The combined area of the lawn and flower bed is 165mē.  What is the width of the flower bed?<BR>\n" );
document.write( "Let x be the width of the flowerbed<BR>\n" );
document.write( "(8+2x)(4+2x)=165<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 #232954 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=232954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2B2x%29%284%2B2x%29=165 ALIGN=MIDDLE  ALT=\"%288%2B2x%29%284%2B2x%29=165\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2B16x%2B8x%2B4x%5E2=165 ALIGN=MIDDLE  ALT=\"32%2B16x%2B8x%2B4x%5E2=165\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2B16x%2B8x%2B4x%5E2-165=0 ALIGN=MIDDLE  ALT=\"32%2B16x%2B8x%2B4x%5E2-165=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 165 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x-133=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x-133=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x-133 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x-133\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=24 ALIGN=MIDDLE  ALT=\"B=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-133 ALIGN=MIDDLE  ALT=\"C=-133\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"x\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2824%29+%2B-+sqrt%28+%2824%29%5E2-4%284%29%28-133%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2824%29+%2B-+sqrt%28+%2824%29%5E2-4%284%29%28-133%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=24 ALIGN=MIDDLE  ALT=\"B=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-133 ALIGN=MIDDLE  ALT=\"C=-133\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B-+sqrt%28+576-4%284%29%28-133%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B-+sqrt%28+576-4%284%29%28-133%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576 ALIGN=MIDDLE  ALT=\"576\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B-+sqrt%28+576--2128+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B-+sqrt%28+576--2128+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%29%28-133%29 ALIGN=MIDDLE  ALT=\"4%284%29%28-133%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2128 ALIGN=MIDDLE  ALT=\"-2128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B-+sqrt%28+576%2B2128+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B-+sqrt%28+576%2B2128+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28576--2128%29 ALIGN=MIDDLE  ALT=\"sqrt%28576--2128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28576%2B2128%29 ALIGN=MIDDLE  ALT=\"sqrt%28576%2B2128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B-+sqrt%28+2704+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B-+sqrt%28+2704+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576 ALIGN=MIDDLE  ALT=\"576\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2128 ALIGN=MIDDLE  ALT=\"2128\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2704 ALIGN=MIDDLE  ALT=\"2704\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B-+sqrt%28+2704+%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B-+sqrt%28+2704+%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B-+52%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B-+52%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2704 ALIGN=MIDDLE  ALT=\"2704\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=52 ALIGN=MIDDLE  ALT=\"52\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+%2B+52%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+%2B+52%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-24+-+52%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-24+-+52%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2828%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%2828%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-76%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=++%28-76%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F2 ALIGN=MIDDLE  ALT=\"x+=+7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-19%2F2 ALIGN=MIDDLE  ALT=\"x+=+-19%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+7%2F2 ALIGN=MIDDLE  ALT=\"x+=+7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-19%2F2 ALIGN=MIDDLE  ALT=\"x+=+-19%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, 'x' is a length. So we'll ignore the negative answer.\r<BR>\n" );
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document.write( "So the width of the flower bed is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7%2F2 ALIGN=MIDDLE  ALT=\"x=7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is 3.5 meters. </SPAN>\n" );
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