document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=909913>Question 909913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A factory is to be built on a lot that measures 80m by 60m. A lawn of uniform width, equal to the area of the factory, must surround it. How wide is the strip of the lawn and what are the dimensions of the factory? (Maybe something to do with using the quadratic formula or factoring?) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #552188 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=552188\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 80*60=4800 m^2<BR>\n" );
document.write( "(80+x)*(60+x)=9600<BR>\n" );
document.write( "x^2+140x+4800 = 9600<BR>\n" );
document.write( "x^2+140x-4800 = 0<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B140x%2B-4800+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B140x%2B-4800+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28140%29%5E2-4%2A1%2A-4800=38800 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28140%29%5E2-4%2A1%2A-4800=38800\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=38800 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-140%2B-sqrt%28+38800+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-140%2B-sqrt%28+38800+%29%29%2F2%5Ca\"   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%5B1%5D+=+%28-%28140%29%2Bsqrt%28+38800+%29%29%2F2%5C1+=+28.488578017961 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28140%29%2Bsqrt%28+38800+%29%29%2F2%5C1+=+28.488578017961\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28140%29-sqrt%28+38800+%29%29%2F2%5C1+=+-168.488578017961 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28140%29-sqrt%28+38800+%29%29%2F2%5C1+=+-168.488578017961\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B140x%2B-4800 ALIGN=MIDDLE  ALT=\"1x%5E2%2B140x%2B-4800\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B140x%2B-4800+=+1%28x-28.488578017961%29%2A%28x--168.488578017961%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B140x%2B-4800+=+1%28x-28.488578017961%29%2A%28x--168.488578017961%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 28.488578017961, -168.488578017961.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B140%2Ax%2B-4800+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B140%2Ax%2B-4800+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " <BR>\n" );
document.write( "x=28.489\r<BR>\n" );
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document.write( "(80+28.489)*(60+28.489)=9600<BR>\n" );
document.write( "(108.489)*(88.489)=9600<BR>\n" );
document.write( "108.489*88.489=9600.083121\r<BR>\n" );
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document.write( " </SPAN>\n" );
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