document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194177>Question 194177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the number of solutions and classify the type of solutions for each of the following equations.  Justify your answer. \r<BR>\n" );
document.write( "\n" );
document.write( "	x2 – 4x - 77 = 0  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145747 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=145747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 -4x -77<BR>\n" );
document.write( ",<BR>\n" );
document.write( "use  discriminate  to  check  number  of  answers<BR>\n" );
document.write( "remember,  D  less  than  0,,,,,no  solutions<BR>\n" );
document.write( ",,,,,,,,,,,,,,,,,,,D  =0,  one  solution<BR>\n" );
document.write( ",,,,,,,,,,,,,,,,,,,D >0,  two  solutions<BR>\n" );
document.write( ",<BR>\n" );
document.write( "a=1,,b=(-4),,c=(-77),,,, D= sqrt ( b^2 - 4 * a * c )<BR>\n" );
document.write( ",<BR>\n" );
document.write( "D  =  sq  rt  ( (-4)^2 - 4 (1) ( -77) ) = sqrt ( 16 + 308 ) =sqrt ( 324) = 18<BR>\n" );
document.write( "therefore,  D >0,,,and  two  solutions<BR>\n" );
document.write( ",<BR>\n" );
document.write( "completing  quadratic  eqn  (  or  factoring  original )<BR>\n" );
document.write( ",<BR>\n" );
document.write( "x = ( 4 +/- 18 )/2  =  11,  and  -7\r<BR>\n" );
document.write( "\n" );
document.write( "checking  by  substituting  both  in  original  eqn ,,both  = 0,,,ok </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );