document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135305>Question 135305</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve for x: 2(8)^(4x)-33(8)^(2x)+16=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99156 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=99156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%288%29%5E%284x%29-33%288%29%5E%282x%29%2B16+=+0 ALIGN=MIDDLE  ALT=\"2%288%29%5E%284x%29-33%288%29%5E%282x%29%2B16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's temporarily substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288%29%5E%282x%29 ALIGN=MIDDLE  ALT=\"z+=+%288%29%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2+=+%288%29%5E%284x%29 ALIGN=MIDDLE  ALT=\"z%5E2+=+%288%29%5E%284x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z%5E2-33z%2B16+=+0 ALIGN=MIDDLE  ALT=\"2z%5E2-33z%2B16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This can be solved for z by factoring.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282z-1%29%28z-16%29+=+0 ALIGN=MIDDLE  ALT=\"%282z-1%29%28z-16%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z-1+=+0 ALIGN=MIDDLE  ALT=\"2z-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-16+=+0 ALIGN=MIDDLE  ALT=\"z-16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we have...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2z+=+1 ALIGN=MIDDLE  ALT=\"2z+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+1%2F2 ALIGN=MIDDLE  ALT=\"z+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+16 ALIGN=MIDDLE  ALT=\"z+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we replace the z with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288%29%5E%282x%29 ALIGN=MIDDLE  ALT=\"z+=+%288%29%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%5E%282x%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%288%29%5E%282x%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2+=+2%5E%28-1%29 ALIGN=MIDDLE  ALT=\"1%2F2+=+2%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so, making these substitutions, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E3%29%5E%282x%29+=+%282%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%282%5E3%29%5E%282x%29+=+%282%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%5E%286x%29+=+%282%29%5E%28-1%29 ALIGN=MIDDLE  ALT=\"%282%29%5E%286x%29+=+%282%29%5E%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Applying the rule: If<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5Ea+=+m%5Eb ALIGN=MIDDLE  ALT=\"m%5Ea+=+m%5Eb\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+b ALIGN=MIDDLE  ALT=\"a+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+-1 ALIGN=MIDDLE  ALT=\"6x+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F6 ALIGN=MIDDLE  ALT=\"x+=+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is one of the roots.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+16 ALIGN=MIDDLE  ALT=\"z+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288%29%5E%282x%29 ALIGN=MIDDLE  ALT=\"z+=+%288%29%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%29%5E%282x%29+=+16 ALIGN=MIDDLE  ALT=\"%288%29%5E%282x%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+2%5E4 ALIGN=MIDDLE  ALT=\"16+=+2%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%5E3%29%5E%282x%29+=+%282%29%5E4 ALIGN=MIDDLE  ALT=\"%282%5E3%29%5E%282x%29+=+%282%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the left side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%5E%286x%29+=+%282%29%5E4 ALIGN=MIDDLE  ALT=\"%282%29%5E%286x%29+=+%282%29%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+=+4 ALIGN=MIDDLE  ALT=\"6x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 6.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4%2F6 ALIGN=MIDDLE  ALT=\"x+=+4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F3 ALIGN=MIDDLE  ALT=\"x+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the second root.<BR>\n" );
document.write( "Solution is: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F6 ALIGN=MIDDLE  ALT=\"x+=+-1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F3 ALIGN=MIDDLE  ALT=\"x+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "I'll leave the check for you to do.  It's not difficult and I've done it myself and the two solutions for x are indeed valid! </SPAN>\n" );
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