document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257059>Question 257059</A>: <I><SPAN STYLE=\"word-break: break-all;\"> imogen wants to make an open top box for packing baked goods by cutting equal squares from each corner of an 11 in. by 14 in. piece of cardboard. she figues that for versatility the area of the bottom must be 80 in^2. what size should she cut from each corner </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189092 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cutting equal squares from each corner of an 11 in. by 14 in. piece of cardboard.<BR>\n" );
document.write( " the area of the bottom must be 80 in^2.<BR>\n" );
document.write( " what size should she cut from each corner<BR>\n" );
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document.write( "x = side of the cutout squares<BR>\n" );
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document.write( "The bottom dimensions of the box will be (11-2x) by (14-2x)<BR>\n" );
document.write( ";<BR>\n" );
document.write( "The area of the bottom given as 80 sq/in, therefore:<BR>\n" );
document.write( ";<BR>\n" );
document.write( "(11-2x)*(14-2x) = 80<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "154 - 22x - 28x + 4x^2 = 80<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "4x^2 - 50x + 154 - 80 = 0<BR>\n" );
document.write( "4x^2 - 50x + 74 = 0<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "2x^2 - 25x + 37 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use the quadratic formula to solve this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "in this problem a=2; b=-25; c=37<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-25%29+%2B-+sqrt%28-25%5E2-4%2A2%2A37+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-25%29+%2B-+sqrt%28-25%5E2-4%2A2%2A37+%29%29%2F%282%2A2%29+\"   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+=+%2825+%2B-+sqrt%28625-296+%29%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B-+sqrt%28625-296+%29%29%2F%284%29+\"   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+=+%2825+%2B-+sqrt%28329+%29%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B-+sqrt%28329+%29%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+%2B+18.138%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B+18.138%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43.138%2F4 ALIGN=MIDDLE  ALT=\"43.138%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 10.78, obviously, this solution is not valid<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+-+18.138%29%2F%284%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+-+18.138%29%2F%284%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.862%2F4 ALIGN=MIDDLE  ALT=\"6.862%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 1.7 inches, the side of the cutout square<BR>\n" );
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document.write( "Check solution on a calc<BR>\n" );
document.write( "Enter (11 - 2(1.7)) * (14 - 2(1.7)) = 80.56 ~ 80 sq/in<BR>\n" );
document.write( " </SPAN>\n" );
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