document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922633>Question 922633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with these. I need to know the equation and why or how it is set up the way it is. Thanks!! <BR>\n" );
document.write( "The sum of two numbers is eleven. The sum of the squares of the two numbers is eighty-five. Find the two numbers. <BR>\n" );
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document.write( "The sum of two numbers is eleven. The sum of the squares of the two numbers is eighty-five. Find the two numbers<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559652 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These kind of problems are done the same way.<BR>\n" );
document.write( "let a & b be the two numbers. Write an equation for each statement<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"The sum of two numbers is eleven.\"<BR>\n" );
document.write( "a + b = 11<BR>\n" );
document.write( "b = (-a+11); use this form for substitution<BR>\n" );
document.write( ": <BR>\n" );
document.write( "\"The sum of the squares of the two numbers is eighty-five.\"<BR>\n" );
document.write( "a^2 + b^2 = 85<BR>\n" );
document.write( "replace b with (-a+11)<BR>\n" );
document.write( "a^2 + (-a+11)^2 = 85<BR>\n" );
document.write( "FOIL (-a+11)(-a+11)<BR>\n" );
document.write( "a^2 + a^2 - 11a - 11a + 121 = 85<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "2a^2 - 22a + 121 - 85 = 0<BR>\n" );
document.write( "a quadratic equation, we can solve<BR>\n" );
document.write( "2a^2 - 22a + 36 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "a^2 - 11a + 18 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(a-2)(a-9) = 0<BR>\n" );
document.write( "two solutions<BR>\n" );
document.write( "a = 2, then b = 9<BR>\n" );
document.write( "a = 9, then b = 2<BR>\n" );
document.write( "\" Find the two numbers.\" 2 & 9<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Did you find you could follow what we did here?<BR>\n" );
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