document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857417>Question 857417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a right triangle has a hypotenuse that is 59 miles long. One side is 1.05 longer than the other. What are the lengths of the two legs  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516612 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=516612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a right triangle has a hypotenuse that is 59 miles long. One side is 1.05 longer than the other. What are the lengths of the two legs <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%2B1.05%29%5E2+=+59%5E2+=+3481 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%2B1.05%29%5E2+=+59%5E2+=+3481\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+2.1x+%2B+1.1025+=+3481 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+2.1x+%2B+1.1025+=+3481\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+2.1x+-+3479.8975+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+2.1x+-+3479.8975+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=2x%5E2%2B2.1x%2B-3479.8975+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2.1x%2B-3479.8975+=+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=%282.1%29%5E2-4%2A2%2A-3479.8975=27843.59 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282.1%29%5E2-4%2A2%2A-3479.8975=27843.59\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=27843.59 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+=+%28-2.1%2B-sqrt%28+27843.59+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2.1%2B-sqrt%28+27843.59+%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-%282.1%29%2Bsqrt%28+27843.59+%29%29%2F2%5C2+=+41.1909966319876 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%282.1%29%2Bsqrt%28+27843.59+%29%29%2F2%5C2+=+41.1909966319876\"   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-%282.1%29-sqrt%28+27843.59+%29%29%2F2%5C2+=+-42.2409966319876 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%282.1%29-sqrt%28+27843.59+%29%29%2F2%5C2+=+-42.2409966319876\"   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=2x%5E2%2B2.1x%2B-3479.8975 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2.1x%2B-3479.8975\"   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=2x%5E2%2B2.1x%2B-3479.8975+=+%28x-41.1909966319876%29%2A%28x--42.2409966319876%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2.1x%2B-3479.8975+=+%28x-41.1909966319876%29%2A%28x--42.2409966319876%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 41.1909966319876, -42.2409966319876.\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%2B2.1%2Ax%2B-3479.8975+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2.1%2Ax%2B-3479.8975+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "x =~ 41.191 miles (the short leg)<BR>\n" );
document.write( "x + 1.05 =~ 42.241 miles\r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );