document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988940>Question 988940</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular skating rink measures 30 m by 14 m. It is to be doubled in area by extending each side by the same amount. Determine how much each side should be extended, </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609405 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609405\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "x=amount each side is increased; L=length=30m; W=width=14m<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(L+x)(W+x)=2LW<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(30m+x)(14m+x)=2(30m)(14m)<BR>\n" );
document.write( "420+44x+x^2=840<BR>\n" );
document.write( "x^2+44x-420=0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B44x%2B-420+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B44x%2B-420+=+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=%2844%29%5E2-4%2A1%2A-420=3616 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2844%29%5E2-4%2A1%2A-420=3616\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3616 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+=+%28-44%2B-sqrt%28+3616+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-44%2B-sqrt%28+3616+%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-%2844%29%2Bsqrt%28+3616+%29%29%2F2%5C1+=+8.06659275674582 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2844%29%2Bsqrt%28+3616+%29%29%2F2%5C1+=+8.06659275674582\"   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-%2844%29-sqrt%28+3616+%29%29%2F2%5C1+=+-52.0665927567458 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2844%29-sqrt%28+3616+%29%29%2F2%5C1+=+-52.0665927567458\"   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%2B44x%2B-420 ALIGN=MIDDLE  ALT=\"1x%5E2%2B44x%2B-420\"   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%2B44x%2B-420+=+1%28x-8.06659275674582%29%2A%28x--52.0665927567458%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B44x%2B-420+=+1%28x-8.06659275674582%29%2A%28x--52.0665927567458%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8.06659275674582, -52.0665927567458.\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%2B44%2Ax%2B-420+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B44%2Ax%2B-420+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "x=8.067m <BR>\n" );
document.write( "ANSWER: Each side should be increased by 8.067 meters.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "(L+x)(W+x)=2LW<BR>\n" );
document.write( "(30m+x)(14m+x)=2(30m)(14m)<BR>\n" );
document.write( "(30m+8.067m)(14m+8.067m)=840m^2<BR>\n" );
document.write( "(38.067m)(22.067m)=840m^2<BR>\n" );
document.write( "840.02m^2=840m^2<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );