document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1015549>Question 1015549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What two numbers when multiplied together equal,  -11250,\r<BR>\n" );
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document.write( "When added together = 125 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #631882 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=631882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A and B are the two numbers<BR>\n" );
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document.write( "A+B=125<BR>\n" );
document.write( "A=125-B<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=-11250 ALIGN=MIDDLE  ALT=\"AB=-11250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28125-B%29%28B%29=-11250 ALIGN=MIDDLE  ALT=\"%28125-B%29%28B%29=-11250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-B%5E2%2B125B=-11250 ALIGN=MIDDLE  ALT=\"-B%5E2%2B125B=-11250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-B%5E2%2B125B%2B11250=0 ALIGN=MIDDLE  ALT=\"-B%5E2%2B125B%2B11250=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=aB%5E2%2BbB%2Bc=0 ALIGN=MIDDLE  ALT=\"aB%5E2%2BbB%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1B%5E2%2B125B%2B11250+=+0 ALIGN=MIDDLE  ALT=\"-1B%5E2%2B125B%2B11250+=+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=B%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"B%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=%28125%29%5E2-4%2A-1%2A11250=60625 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28125%29%5E2-4%2A-1%2A11250=60625\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=60625 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+=+%28-125%2B-sqrt%28+60625+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-125%2B-sqrt%28+60625+%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=B%5B1%5D+=+%28-%28125%29%2Bsqrt%28+60625+%29%29%2F2%5C-1+=+-60.6107225224513 ALIGN=MIDDLE  ALT=\"B%5B1%5D+=+%28-%28125%29%2Bsqrt%28+60625+%29%29%2F2%5C-1+=+-60.6107225224513\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5B2%5D+=+%28-%28125%29-sqrt%28+60625+%29%29%2F2%5C-1+=+185.610722522451 ALIGN=MIDDLE  ALT=\"B%5B2%5D+=+%28-%28125%29-sqrt%28+60625+%29%29%2F2%5C-1+=+185.610722522451\"   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=-1B%5E2%2B125B%2B11250 ALIGN=MIDDLE  ALT=\"-1B%5E2%2B125B%2B11250\"   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=-1B%5E2%2B125B%2B11250+=+-1%28B--60.6107225224513%29%2A%28B-185.610722522451%29 ALIGN=MIDDLE  ALT=\"-1B%5E2%2B125B%2B11250+=+-1%28B--60.6107225224513%29%2A%28B-185.610722522451%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -60.6107225224513, 185.610722522451.\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%2B125%2Ax%2B11250+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B125%2Ax%2B11250+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "B=-60.6107 or 185.6107<BR>\n" );
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document.write( "A=125-(-60.6107)=185.6107 <BR>\n" );
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document.write( "ANSWER: The two numbers are 185.6107 and -60.6107.<BR>\n" );
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document.write( "CHECK:<BR>\n" );
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document.write( "AB=-11250<BR>\n" );
document.write( "(185.6107)(-60.6107)=-11250<BR>\n" );
document.write( "11249.9945=11250 (error due to rounding roots)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );