document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619309>Question 619309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x² + 12x + 11<BR>\n" );
document.write( "I'm assuming you meant: <BR>\n" );
document.write( "x² + 12x + 11 = 0  (Yes, the zero matters  ;-) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389927 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389927\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x² + 12x + 11 = 0<BR>\n" );
document.write( "(x + ...) (x + ... ) = 0<BR>\n" );
document.write( "We need to find two factors of 11 whose sum is 12.  That's rather easy since 11 is prime.  It's only factors are 1 and itself - 11.<BR>\n" );
document.write( "(x + 11)(x + 1) = 0<BR>\n" );
document.write( "Now solve each of these separately.  That is, at least one of these two factors must be zero for the whole equation to be equal to zero.<BR>\n" );
document.write( "(x+11) = 0<BR>\n" );
document.write( "Subtract 11 from both sides ... <BR>\n" );
document.write( "x = -11<BR>\n" );
document.write( "Now the other ... <BR>\n" );
document.write( "x+1 = 0<BR>\n" );
document.write( "Subtract 1 from both sides ... <BR>\n" );
document.write( "x = -1\r<BR>\n" );
document.write( "\n" );
document.write( "So both -11 and -1 are possible solutions for x.  Let's check ... \r<BR>\n" );
document.write( "\n" );
document.write( "x² + 12x + 11 = 0<BR>\n" );
document.write( "(-11)^2 + 12(-11) + 11 = 0<BR>\n" );
document.write( "121 - 132 + 11 = 0<BR>\n" );
document.write( "0 = 0 Check!\r<BR>\n" );
document.write( "\n" );
document.write( "x² + 12x + 11 = 0<BR>\n" );
document.write( "(-1)^2 + 12(-1) + 11 = 0<BR>\n" );
document.write( "1 - 12 + 11 = 0<BR>\n" );
document.write( "0 = 0 Check! </SPAN>\n" );
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