document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925026>Question 925026</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of five times a number and five times its square is 210. Determine the numbers  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561273 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=561273\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let n be the number we want.<BR>\n" );
document.write( "Then we have<BR>\n" );
document.write( "(1) 5n + 5n^2 = 210 or after dividing both sides by 5 we have<BR>\n" );
document.write( "(2) n + n^2 = 42 or<BR>\n" );
document.write( "(3) n^2 + n - 42 = 0<BR>\n" );
document.write( "Now factor (3) and get<BR>\n" );
document.write( "(4) (n+7)*(n-6) = 0, giving us the roots <BR>\n" );
document.write( "(5) n = -7,6<BR>\n" );
document.write( "Let's check the answers with (1).<BR>\n" );
document.write( "Is (5*(-7) + 5*(-7)^2 = 210)?<BR>\n" );
document.write( "Is (-35 + 5*49 = 210)?<BR>\n" );
document.write( "Is (-35 + 245 = 210)?<BR>\n" );
document.write( "Is (210 = 210)? Yes<BR>\n" );
document.write( "Is (5*(6) + 5*(6)^2 = 210)?<BR>\n" );
document.write( "Is (30 + 5*36 = 210)?<BR>\n" );
document.write( "Is (30 + 180 = 210)?<BR>\n" );
document.write( "Is (210 = 210)? Yes<BR>\n" );
document.write( "Answer: The set {-7,6} satisfies the problem statement. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );