document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196132>Question 196132</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is from Activity Bank, INTEGRATED MATHEMATICS 1 Copyright by Houghton Mifflin Company.\r<BR>\n" );
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document.write( "The city of Casablanca, Morocco has the world's largest swimming pool.  The distance between two opposite corners of the pool is about 1590 ft. The length is about 1325 ft. longer than the width.  What are the length and width of the pool? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147070 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=147070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance between two opposite corners of the pool is about 1590 ft. The length is about 1325 ft. longer than the width. What are the length and width of the pool?<BR>\n" );
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document.write( "Because the pool is rectangular you can apply Pythagorean theorem:<BR>\n" );
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document.write( "Let w = width<BR>\n" );
document.write( "then<BR>\n" );
document.write( "w+1325 = length<BR>\n" );
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document.write( "w^2 + (w+1325)^2 = 1590^2<BR>\n" );
document.write( "w^2 + (w+1325)(w+1325) = 1590^2<BR>\n" );
document.write( "w^2 + (w^2+2650w+1755625) = 2528100<BR>\n" );
document.write( "2w^2 + 2650w + 1755625 = 2528100<BR>\n" );
document.write( "2w^2 + 2650w - 772475 = 0<BR>\n" );
document.write( "Solving using the quadratic equation yields:<BR>\n" );
document.write( "w = {245.87, -1570.87}<BR>\n" );
document.write( "We can throw out the negative solution leaving:<BR>\n" );
document.write( "w = 245.87 feet (width)<BR>\n" );
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document.write( "length:<BR>\n" );
document.write( "w+1325 = 245.87+1325 = 1570.87 feet (length)<BR>\n" );
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document.write( "Details of quadratic follows:<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=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=2w%5E2%2B2650w%2B-772475+=+0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2650w%2B-772475+=+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=%282650%29%5E2-4%2A2%2A-772475=13202300 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282650%29%5E2-4%2A2%2A-772475=13202300\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=13202300 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+=+%28-2650%2B-sqrt%28+13202300+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2650%2B-sqrt%28+13202300+%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-%282650%29%2Bsqrt%28+13202300+%29%29%2F2%5C2+=+245.874234553138 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%282650%29%2Bsqrt%28+13202300+%29%29%2F2%5C2+=+245.874234553138\"   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-%282650%29-sqrt%28+13202300+%29%29%2F2%5C2+=+-1570.87423455314 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%282650%29-sqrt%28+13202300+%29%29%2F2%5C2+=+-1570.87423455314\"   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=2w%5E2%2B2650w%2B-772475 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2650w%2B-772475\"   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=2w%5E2%2B2650w%2B-772475+=+2%28w-245.874234553138%29%2A%28w--1570.87423455314%29 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2650w%2B-772475+=+2%28w-245.874234553138%29%2A%28w--1570.87423455314%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 245.874234553138, -1570.87423455314.\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+2%2Ax%5E2%2B2650%2Ax%2B-772475+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2650%2Ax%2B-772475+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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