document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956947>Question 956947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man is three times as old as his son. Ten years ago the sum of the square of their ages was 1250. find their ages<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584723 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=584723\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> M=man's age; S=son's age<BR>\n" );
document.write( "M=3S<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28M-10%29%5E2%2B%28S-10%29%5E2=1250 ALIGN=MIDDLE  ALT=\"%28M-10%29%5E2%2B%28S-10%29%5E2=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute for M<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283S-10%29%5E2%2B%28S-10%29%5E2=1250 ALIGN=MIDDLE  ALT=\"%283S-10%29%5E2%2B%28S-10%29%5E2=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9S%5E2-60S%2B100%2BS%5E2-20S%2B100=1250 ALIGN=MIDDLE  ALT=\"9S%5E2-60S%2B100%2BS%5E2-20S%2B100=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10S%5E2-80S%2B200=1250 ALIGN=MIDDLE  ALT=\"10S%5E2-80S%2B200=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1250 from each side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10S%5E2-80S-1050=0 ALIGN=MIDDLE  ALT=\"10S%5E2-80S-1050=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=aS%5E2%2BbS%2Bc=0 ALIGN=MIDDLE  ALT=\"aS%5E2%2BbS%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10S%5E2%2B-80S%2B-1050+=+0 ALIGN=MIDDLE  ALT=\"10S%5E2%2B-80S%2B-1050+=+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=S%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"S%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%2A10%2A-1050=48400 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-80%29%5E2-4%2A10%2A-1050=48400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=48400 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+48400+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--80%2B-sqrt%28+48400+%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=S%5B1%5D+=+%28-%28-80%29%2Bsqrt%28+48400+%29%29%2F2%5C10+=+15 ALIGN=MIDDLE  ALT=\"S%5B1%5D+=+%28-%28-80%29%2Bsqrt%28+48400+%29%29%2F2%5C10+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B2%5D+=+%28-%28-80%29-sqrt%28+48400+%29%29%2F2%5C10+=+-7 ALIGN=MIDDLE  ALT=\"S%5B2%5D+=+%28-%28-80%29-sqrt%28+48400+%29%29%2F2%5C10+=+-7\"   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=10S%5E2%2B-80S%2B-1050 ALIGN=MIDDLE  ALT=\"10S%5E2%2B-80S%2B-1050\"   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=10S%5E2%2B-80S%2B-1050+=+10%28S-15%29%2A%28S--7%29 ALIGN=MIDDLE  ALT=\"10S%5E2%2B-80S%2B-1050+=+10%28S-15%29%2A%28S--7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 15, -7.\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+10%2Ax%5E2%2B-80%2Ax%2B-1050+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B-80%2Ax%2B-1050+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "S=15 ANSWER The son is 15 years old.<BR>\n" );
document.write( "M=3S=3(15yrs)=45yrs ANSWER 2: The man is 45 years old.<BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28M-10%29%5E2%2B%28S-10%29%5E2=1250 ALIGN=MIDDLE  ALT=\"%28M-10%29%5E2%2B%28S-10%29%5E2=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2845-10%29%5E2%2B%2815-10%29%5E2=1250 ALIGN=MIDDLE  ALT=\"%2845-10%29%5E2%2B%2815-10%29%5E2=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%5E2%2B5%5E2=1250 ALIGN=MIDDLE  ALT=\"35%5E2%2B5%5E2=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1225%2B25=1250 ALIGN=MIDDLE  ALT=\"1225%2B25=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1250=1250 ALIGN=MIDDLE  ALT=\"1250=1250\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );