document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193575>Question 193575</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm sorry.  I know this problem is very similar to the example, but I get a very crazy answer when I've tried to do this like the example many times.  I must be doing something wrong.  Please help. \r<BR>\n" );
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document.write( "One leg of a right triangle is 96 inches.  Find the hypotenuse and teh other leg if the length of the hypotenuse exceeds 2 and 1/2 times teh other leg by 4 inches.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145298 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=145298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One leg of a right triangle is 96 inches. Find the hypotenuse and teh other leg if the length of the hypotenuse exceeds 2 and 1/2 times teh other leg by 4 inches.<BR>\n" );
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document.write( "Let x = length of \"other leg\" of triangle<BR>\n" );
document.write( "then <BR>\n" );
document.write( "(5/2)x-4 = hypotenuse<BR>\n" );
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document.write( "The applying the Pythagorean theorem:<BR>\n" );
document.write( "x^2 + ((5/2)x-4) = 96^2<BR>\n" );
document.write( "x^2 + ((5/2)x-4)((5/2)x-4) = 96^2<BR>\n" );
document.write( "x^2 + (25/4)x^2-20x +16 = 96^2<BR>\n" );
document.write( "(29/4)x^2-20x +16 = 9216<BR>\n" );
document.write( "(29/4)x^2-20x -9200 = 0<BR>\n" );
document.write( "29x^2 - 80x -36800 = 0<BR>\n" );
document.write( "Solving using the quadratic equation we get:<BR>\n" );
document.write( "x ={37.03, -34.26}<BR>\n" );
document.write( "Throwing away the negative solution we're left with:<BR>\n" );
document.write( "x = 37.03 inches (other leg)<BR>\n" );
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document.write( "Hypotenuse:<BR>\n" );
document.write( "(5/2)x-4 = (5/2)37.03-4 = 88.58 inches (hypotenuse)<BR>\n" );
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document.write( "Details of the quadratic equation:<BR>\n" );
document.write( "<TABLE  BORDER=1>\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=29x%5E2%2B-80x%2B-36800+=+0 ALIGN=MIDDLE  ALT=\"29x%5E2%2B-80x%2B-36800+=+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=%28-80%29%5E2-4%2A29%2A-36800=4275200 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-80%29%5E2-4%2A29%2A-36800=4275200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4275200 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--80%2B-sqrt%28+4275200+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--80%2B-sqrt%28+4275200+%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-%28-80%29%2Bsqrt%28+4275200+%29%29%2F2%5C29+=+37.028546160883 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-80%29%2Bsqrt%28+4275200+%29%29%2F2%5C29+=+37.028546160883\"   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-%28-80%29-sqrt%28+4275200+%29%29%2F2%5C29+=+-34.2699254712278 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-80%29-sqrt%28+4275200+%29%29%2F2%5C29+=+-34.2699254712278\"   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=29x%5E2%2B-80x%2B-36800 ALIGN=MIDDLE  ALT=\"29x%5E2%2B-80x%2B-36800\"   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=29x%5E2%2B-80x%2B-36800+=+29%28x-37.028546160883%29%2A%28x--34.2699254712278%29 ALIGN=MIDDLE  ALT=\"29x%5E2%2B-80x%2B-36800+=+29%28x-37.028546160883%29%2A%28x--34.2699254712278%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 37.028546160883, -34.2699254712278.\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+29%2Ax%5E2%2B-80%2Ax%2B-36800+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+29%2Ax%5E2%2B-80%2Ax%2B-36800+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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