document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964084>Question 964084</A>: <I><SPAN STYLE=\"word-break: break-all;\">  positive integer is 11 more than 28 times another. Their product is 11420. Find the two integers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #589024 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=589024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set x = the larger number<BR>\n" );
document.write( " y = the smaller number<BR>\n" );
document.write( "x = 11 + 28y<BR>\n" );
document.write( "x*y = 11420<BR>\n" );
document.write( "substitute ( 11+28y ) for x\r<BR>\n" );
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document.write( "( 11+28y )y =11420<BR>\n" );
document.write( "11y + 28y^2 = 11420<BR>\n" );
document.write( "28y^2 + 11y - 11420 = 0\r<BR>\n" );
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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=28x%5E2%2B11x%2B-11420+=+0 ALIGN=MIDDLE  ALT=\"28x%5E2%2B11x%2B-11420+=+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=%2811%29%5E2-4%2A28%2A-11420=1279161 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2811%29%5E2-4%2A28%2A-11420=1279161\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1279161 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+=+%28-11%2B-sqrt%28+1279161+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-11%2B-sqrt%28+1279161+%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-%2811%29%2Bsqrt%28+1279161+%29%29%2F2%5C28+=+20 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2811%29%2Bsqrt%28+1279161+%29%29%2F2%5C28+=+20\"   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-%2811%29-sqrt%28+1279161+%29%29%2F2%5C28+=+-20.3928571428571 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2811%29-sqrt%28+1279161+%29%29%2F2%5C28+=+-20.3928571428571\"   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=28x%5E2%2B11x%2B-11420 ALIGN=MIDDLE  ALT=\"28x%5E2%2B11x%2B-11420\"   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=28x%5E2%2B11x%2B-11420+=+28%28x-20%29%2A%28x--20.3928571428571%29 ALIGN=MIDDLE  ALT=\"28x%5E2%2B11x%2B-11420+=+28%28x-20%29%2A%28x--20.3928571428571%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 20, -20.3928571428571.\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+28%2Ax%5E2%2B11%2Ax%2B-11420+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+28%2Ax%5E2%2B11%2Ax%2B-11420+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Based upon solver solution above, y = 20<BR>\n" );
document.write( "Since x*y = 11420,<BR>\n" );
document.write( "x = 11420/20<BR>\n" );
document.write( "x = 571 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );