document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992164>Question 992164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem leading to quadractic<BR>\n" );
document.write( "The sum of the digits of a two-digit number is 14. The tens digit is the square of a number which is 2 less than the units digit. Find the two-digit number. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611839 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=611839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let t = the ten's digit<BR>\n" );
document.write( "let u = the units<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The sum of the digits of a two-digit number is 14.<BR>\n" );
document.write( "t + u = 14<BR>\n" );
document.write( "or<BR>\n" );
document.write( "t = (14-u); use this form for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( " The tens digit is the square of a number which is 2 less than the units digit.<BR>\n" );
document.write( "t = (u-2)^2<BR>\n" );
document.write( "FOIL (u-2)(u-2)<BR>\n" );
document.write( "t = u^2 - 4u + 4<BR>\n" );
document.write( "Replace t with (14-u)<BR>\n" );
document.write( "14 - u = u^2 - 4u + 4<BR>\n" );
document.write( "0 = u^2 - 4u + u + 4 - 14<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "u^2 - 3u - 10 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(u-5)(u+2) = 0<BR>\n" );
document.write( "The positive solution is what we want here<BR>\n" );
document.write( "u = 5<BR>\n" );
document.write( "then<BR>\n" );
document.write( "t = 14 - 5<BR>\n" );
document.write( " t = 9<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Find the two-digit number. 95<BR>\n" );
document.write( ":<BR>\n" );
document.write( ";<BR>\n" );
document.write( "we can confirm this, in the 2nd statement<BR>\n" );
document.write( "\"The tens digit is the square of a number which is 2 less than the units digit.\" <BR>\n" );
document.write( "9 = (5-2)^2<BR>\n" );
document.write( "9 = 3^2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );