document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=542571>Question 542571</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the equation by making an appropriate substitution.<BR>\n" );
document.write( "x-512-16sqrtx=0<BR>\n" );
document.write( "here is what I have tried:<BR>\n" );
document.write( "x^1-16x^1/2-512<BR>\n" );
document.write( "(x^1/2)^2-16^1/2-512<BR>\n" );
document.write( "subsitute x for u<BR>\n" );
document.write( "u^2-16u-512<BR>\n" );
document.write( "factor (I cannot find a factor for this problem so I divide everything by 2)<BR>\n" );
document.write( "u^2-8u-256<BR>\n" );
document.write( "using the formula<BR>\n" );
document.write( "8 +-sqrt8^2-4(1)(256)/2(1)<BR>\n" );
document.write( "8 +-sqrrt1088 / 2<BR>\n" );
document.write( "reduced<BR>\n" );
document.write( "4+12sqrrt17,   4-12sqrrt17<BR>\n" );
document.write( "my answer choices are<BR>\n" );
document.write( "{768}<BR>\n" );
document.write( "{2068}<BR>\n" );
document.write( "{1024}<BR>\n" );
document.write( "{512}<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354636 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=354636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're ok up the point of substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+x%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"u+=+x%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"u+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2-16u-512+=+0 ALIGN=MIDDLE  ALT=\"u%5E2-16u-512+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This wil factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u%2B16%29%28u-32%29+=+0 ALIGN=MIDDLE  ALT=\"%28u%2B16%29%28u-32%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product rule.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%2B16+=+0 ALIGN=MIDDLE  ALT=\"u%2B16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u-32+=+0 ALIGN=MIDDLE  ALT=\"u-32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+-16 ALIGN=MIDDLE  ALT=\"u+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+32 ALIGN=MIDDLE  ALT=\"u+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+sqrt%28x%29 ALIGN=MIDDLE  ALT=\"u+=+sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+=+-16 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29+=+32 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides in each case.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+256%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+256%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x+=+1024%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x+=+1024%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You should check these solutions because, in squaring, you may have inadvertently introduced invalid solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-512-16sqrt%28x%29+=+0 ALIGN=MIDDLE  ALT=\"x-512-16sqrt%28x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+256 ALIGN=MIDDLE  ALT=\"x+=+256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256-512-16sqrt%28256%29+=+0 ALIGN=MIDDLE  ALT=\"256-512-16sqrt%28256%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256-512-16%2A16+=+0 ALIGN=MIDDLE  ALT=\"256-512-16%2A16+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256-512-256+=+0 ALIGN=MIDDLE  ALT=\"256-512-256+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-512+%3C%3E+0 ALIGN=MIDDLE  ALT=\"-512+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024-512-16sqrt%281024%29+=+0 ALIGN=MIDDLE  ALT=\"1024-512-16sqrt%281024%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024-512-16%2A32+=+0 ALIGN=MIDDLE  ALT=\"1024-512-16%2A32+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024-512-512+=+0 ALIGN=MIDDLE  ALT=\"1024-512-512+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024-1024+=+0 ALIGN=MIDDLE  ALT=\"1024-1024+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );