document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=168386>Question 168386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem:\r<BR>\n" );
document.write( "\n" );
document.write( "     A rectangular pond measures 3m by 5m. A concrete walk of uniform width is constructed around the pond. If the walk and pond together cover an area of 39m^2, how wide is the walk? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #124118 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=124118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular pond measures 3m by 5m. A concrete walk of uniform width is constructed around the pond. If the walk and pond together cover an area of 39m^2, how wide is the walk?<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let w = width of walk<BR>\n" );
document.write( ".<BR>\n" );
document.write( "width of pond w/walk = 3+2w<BR>\n" );
document.write( "length of pond w/walk = 5+2w<BR>\n" );
document.write( ".<BR>\n" );
document.write( "39 = (3+2w)(5+2w)<BR>\n" );
document.write( "39 = 15 + 6w + 10w + 4w^2<BR>\n" );
document.write( "39 = 15 + 16w + 4w^2<BR>\n" );
document.write( "0 = -24 + 16w + 4w^2<BR>\n" );
document.write( "0 = 4w^2 + 16w - 24<BR>\n" );
document.write( "0 = w^2 + 4w - 6<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the quadratic equation to solve we get:<BR>\n" );
document.write( "x = {1.162, -5.162}<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We can toss out the negative answer leaving us with:<BR>\n" );
document.write( "1.162 meters (width of walk)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Here's the details of the quadratic:<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=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1w%5E2%2B4w%2B-6+=+0 ALIGN=MIDDLE  ALT=\"1w%5E2%2B4w%2B-6+=+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=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%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=%284%29%5E2-4%2A1%2A-6=40 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A1%2A-6=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=40 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+=+%28-4%2B-sqrt%28+40+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4%2B-sqrt%28+40+%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=w%5B1%5D+=+%28-%284%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+1.16227766016838 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%284%29%2Bsqrt%28+40+%29%29%2F2%5C1+=+1.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%284%29-sqrt%28+40+%29%29%2F2%5C1+=+-5.16227766016838 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%284%29-sqrt%28+40+%29%29%2F2%5C1+=+-5.16227766016838\"   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=1w%5E2%2B4w%2B-6 ALIGN=MIDDLE  ALT=\"1w%5E2%2B4w%2B-6\"   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=1w%5E2%2B4w%2B-6+=+1%28w-1.16227766016838%29%2A%28w--5.16227766016838%29 ALIGN=MIDDLE  ALT=\"1w%5E2%2B4w%2B-6+=+1%28w-1.16227766016838%29%2A%28w--5.16227766016838%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.16227766016838, -5.16227766016838.\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%2B4%2Ax%2B-6+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );