document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112951>Question 1112951</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) Factorise: 2^2x -7 • 2^x -8 = 0<BR>\n" );
document.write( "B) fund the value(s) for x in part a </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727993 by </B><A HREF=/tutors/aboutme.mpl?userid=Benbuks><B>Benbuks(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Benbuks><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=727993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) Factorise: 2^2x -7 • 2^x -8 = 0<BR>\n" );
document.write( "B) fund the value(s) for x in part a\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "      SOLUTION\r<BR>\n" );
document.write( "\n" );
document.write( "A) To factorize\r<BR>\n" );
document.write( "\n" );
document.write( " 2^2x -7 • 2^x -8 = 0\r<BR>\n" );
document.write( "\n" );
document.write( "this  equation can be written as<BR>\n" );
document.write( " <BR>\n" );
document.write( "(2^x)² - 7•2^x -8 =0 \r<BR>\n" );
document.write( "\n" );
document.write( "let p=2^x .( so any where 2^x is present in the equation,  we replace it with p) . \r<BR>\n" );
document.write( "\n" );
document.write( "by doing so, we would have \r<BR>\n" );
document.write( "\n" );
document.write( "p² -7p -8=0 \r<BR>\n" );
document.write( "\n" );
document.write( "because this is a now a quadratic equation,  we would have two possible factors that satisfy the equation above . And they're -8 and 1<BR>\n" );
document.write( " ( by inspection ) . You could however use the quadratic formula if you are not sure which factor to use .\r<BR>\n" );
document.write( "\n" );
document.write( "Now, \r<BR>\n" );
document.write( "\n" );
document.write( "p² -7p -8=0 \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; p² -8p + p -8 =0 \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; P(p-8) +1(p-8) =0 \r<BR>\n" );
document.write( "\n" );
document.write( "( p-8) is common ,so we pull it out \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; (p-8)(p+1)=0\r<BR>\n" );
document.write( "\n" );
document.write( "&#8756; ( 2^x -8)(2^x + 1)=0 ...( Factorized ) <BR>\n" );
document.write( " <BR>\n" );
document.write( "B)  we seek the possible real values of x \r<BR>\n" );
document.write( "\n" );
document.write( "from   ( 2^x -8)(2^x + 1)=0\r<BR>\n" );
document.write( "\n" );
document.write( "for this to hold , it means that \r<BR>\n" );
document.write( "\n" );
document.write( " ( 2^x -8) =0  or (2^x + 1)=0\r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; 2^x =8  \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; 2^x = 2³\r<BR>\n" );
document.write( "\n" );
document.write( " 2 on both sides cancels\r<BR>\n" );
document.write( "\n" );
document.write( "we have \r<BR>\n" );
document.write( "\n" );
document.write( "x= 3  \r<BR>\n" );
document.write( "\n" );
document.write( "for the other case ,\r<BR>\n" );
document.write( "\n" );
document.write( "2^x =-1 <BR>\n" );
document.write( "take square on both sides\r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; 2^(2x) = 1 \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594;2^(2x) = 2^0 \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; 2x=0 \r<BR>\n" );
document.write( "\n" );
document.write( "&#8594; x= 0 <BR>\n" );
document.write( "but this  value doesn't satisfy the\r<BR>\n" );
document.write( "\n" );
document.write( " equation,  hence we pick x=3 as our answer \r<BR>\n" );
document.write( "\n" );
document.write( "&#8756; ANSWER :X=3  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );