document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130599>Question 130599</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131808583/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this equation: the area of a frame is equal to the area of 4\"x6\" photo it surrounds. the frame is of uniform width. how wide is the frame? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95391 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=95391\">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=drawing%28400%2C400%2C-1%2C10%2C-1%2C10%2C%0D%0Arectangle%280%2C0%2C6%2C8%29%2C%0D%0Arectangle%281%2C1%2C5%2C7%29%2C%0D%0Alocate%281.5%2C4.5%2C6+in%29%2C%0D%0Alocate%286.5%2C4.5%2C6+%2B+2x%29%2C%0D%0Aline%286.5%2C0%2C6.5%2C4.1%29%2C%0D%0Aline%286.5%2C0%2C6.3%2C.3%29%2C%0D%0Aline%286.5%2C0%2C6.7%2C.3%29%2C%0D%0Aline%286.5%2C8%2C6.3%2C7.7%29%2C%0D%0Aline%286.5%2C8%2C6.7%2C7.7%29%2C%0D%0Aline%286.5%2C4.7%2C6.5%2C8%29%2C%0D%0Alocate%28.5%2C4.5%2Cx%29%2C%0D%0Alocate%282.5%2C1.5%2C4+in%29%2C%0D%0Alocate%282.5%2C-.3%2C4+%2B+2x%29%2C%0D%0Aline%280%2C-.5%2C2.2%2C-.5%29%2C%0D%0Aline%280%2C-.5%2C.3%2C-.2%29%2C%0D%0Aline%280%2C-.5%2C.3%2C-.8%29%2C%0D%0Aline%284%2C-.5%2C6%2C-.5%29%2C%0D%0Aline%286%2C-.5%2C5.7%2C-.2%29%2C%0D%0Aline%286%2C-.5%2C5.7%2C-.8%29%2C%0D%0Alocate%282.8%2C.7%2Cx%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The outside dimensions of the frame, as we can see from the picture are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B2x ALIGN=MIDDLE  ALT=\"6%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+%2B+2x ALIGN=MIDDLE  ALT=\"4+%2B+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the area of the overall thing, frame and the picture inside must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B2x%29%284%2B2x%29 ALIGN=MIDDLE  ALT=\"%286%2B2x%29%284%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the area covered by the frame only must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B2x%29%284%2B2x%29-%286%2A4%29 ALIGN=MIDDLE  ALT=\"%286%2B2x%29%284%2B2x%29-%286%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, because we have to subtract the area of the picture.  It is also given that this area must be equal to the picture it surrounds, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A4=24 ALIGN=MIDDLE  ALT=\"6%2A4=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B2x%29%284%2B2x%29-24=24 ALIGN=MIDDLE  ALT=\"%286%2B2x%29%284%2B2x%29-24=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Apply FOIL and put everything on the left:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2B12x%2B8x%2B4x%5E2-24-24=0 ALIGN=MIDDLE  ALT=\"24%2B12x%2B8x%2B4x%5E2-24-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Collect terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B20x-24=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B20x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by 4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-6=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula because there are no rational factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-6%29+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-6%29+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+16%2B24+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16%2B24+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+40+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+40+%29%29%2F%282%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=-2%2B-sqrt%2810%29 ALIGN=MIDDLE  ALT=\"x=-2%2B-sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2-sqrt%2810%29%3C0 ALIGN=MIDDLE  ALT=\"-2-sqrt%2810%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so exclude this root -- we are looking for a positive number measure of length.\r<BR>\n" );
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document.write( "Therefore the width of the frame (x in the figure) is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"-2%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches or approximately 1.16 inches. </SPAN>\n" );
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