document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=513646>Question 513646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide 12 into two parts such that the sum of their squares is 74. We need to 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 #343094 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=343094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = one of the numbers<BR>\n" );
document.write( "Then the other number = 12 - x<BR>\n" );
document.write( "Sum of the squares is 74:<BR>\n" );
document.write( "x^2 + (12-x)^2 = 74<BR>\n" );
document.write( "Solve for x:<BR>\n" );
document.write( "x^2 + 144 - 24x + x^2 = 74<BR>\n" );
document.write( "2x^2 - 24x + 70 = 0<BR>\n" );
document.write( "x^2 - 12x + 35 = 0<BR>\n" );
document.write( "Factor:<BR>\n" );
document.write( "(x-7)(x-5) = 0<BR>\n" );
document.write( "So the numbers are 5 and 7 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );