document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=724086>Question 724086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the maximum product of two numbers that add to 18? What numbers yield this product? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443580 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=443580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two numbers, p=xy, and x+y=18, so y=18-x.  Substitute to see p=x(18-x), p=18x-x^2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=-x%5E2%2B18x%29 ALIGN=MIDDLE  ALT=\"highlight%28p=-x%5E2%2B18x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "p is a function of x and it has a maximum.  How to solve the rest depends on choosing basic Algebra or choosing Calculus using a derivative.  \r<BR>\n" );
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document.write( "Completing the Square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818%2F2%29%5E2=81%29%29%29.++That+would+be+the+square+term+to+add+%26+subtract.%0D%0A%0D%0A%7B%7B%7B-x%5E2%2B18x=%28-1%29%28x%5E2-18x+%2B+81%29+%2B81 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  (Because when multiply by -1, sign changes).<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%28x-9%29%5E2%2B81 ALIGN=MIDDLE  ALT=\"-1%28x-9%29%5E2%2B81\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=-1%28x-9%29%5E2%2B81%29 ALIGN=MIDDLE  ALT=\"highlight%28p=-1%28x-9%29%5E2%2B81%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ANSWER: The MAXIMUM will be at x=9, where p=81<BR>\n" );
document.write( "Note: Some of this solution is NOT being rendered correctly in the system but I DID write it correctly. </SPAN>\n" );
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