document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174930>Question 1174930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this equation<BR>\n" );
document.write( "2. The sum of two numbers is 23 and their product is 120. find the two numbers  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800435 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800435\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Informally first....<br><BR>\n" );
document.write( "Look at pairs of numbers with a sum of 23 and find a pair with a product of 120.<br><BR>\n" );
document.write( "You can shorten the search by noting that, with a product of 120, one of the numbers must be a multiple of 5.  So the numbers are either 5 and 18 or 15 and 8.<br><BR>\n" );
document.write( "5*18 = 90; 15*8 = 120.  So the two numbers are 15 and 8.<br><BR>\n" );
document.write( "-----------------------------------------------<br><BR>\n" );
document.write( "Now using formal algebra....<br><BR>\n" );
document.write( "let x be one of the two numbers<BR>\n" );
document.write( "then 23-x is the other (because their sum is 23)<br><BR>\n" );
document.write( "The product of the two numbers is 120:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2823-x%29+=+120 ALIGN=MIDDLE  ALT=\"x%2823-x%29+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23x-x%5E2+=+120 ALIGN=MIDDLE  ALT=\"23x-x%5E2+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-23x%2B120+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-23x%2B120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "To solve this algebraically, you need to factor the quadratic expression by finding two numbers whose sum is 23 and whose product is 120.<br><BR>\n" );
document.write( "But that's what you had to do with the original problem!<br><BR>\n" );
document.write( "So the formal algebraic approach doesn't get you any closer to the solution of the problem.<br><BR>\n" );
document.write( "However, you should understand the process for solving the problem algebraically.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-23x%2B120+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-23x%2B120+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-15%29%28x-8%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-15%29%28x-8%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+15 ALIGN=MIDDLE  ALT=\"x+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8 ALIGN=MIDDLE  ALT=\"x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );