document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=504028>Question 504028</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two integers whose sum is 23 and whose product is 90. Show work.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339490 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x & y are two integers.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x+y = 23<BR>\n" );
document.write( "so<BR>\n" );
document.write( "y = 23-x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x*y = 90<BR>\n" );
document.write( ".<BR>\n" );
document.write( "substitute y = 23-x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x*(23-x) = 90<BR>\n" );
document.write( "23 -x^2 = 90<BR>\n" );
document.write( "-x^2 +23 -90 = 0<BR>\n" );
document.write( "(-x + 5)(x - 18) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Check the factoring using FOIL<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-x^2 +18x +5x -90<BR>\n" );
document.write( "OK<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x = 5 or 18<BR>\n" );
document.write( "which means<BR>\n" );
document.write( "y = 18 or 5, respectively,<BR>\n" );
document.write( "which ensures x+y = 23<BR>\n" );
document.write( ".<BR>\n" );
document.write( "and we just showed that 5*18 =90<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So the two integers are 5 and 18.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );