document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=186689>Question 186689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^-4-3x^-2-4=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #139950 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=139950\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-4%29-3x%5E%28-2%29-4=0 ALIGN=MIDDLE  ALT=\"x%5E%28-4%29-3x%5E%28-2%29-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%5E%28-2%29 ALIGN=MIDDLE  ALT=\"z=x%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2=x%5E%28-4%29 ALIGN=MIDDLE  ALT=\"z%5E2=x%5E%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2-3z-4=0 ALIGN=MIDDLE  ALT=\"z%5E2-3z-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-4%29 ALIGN=MIDDLE  ALT=\"x%5E%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2 ALIGN=MIDDLE  ALT=\"z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=az%5E2%2Bbz%2Bc ALIGN=MIDDLE  ALT=\"az%5E2%2Bbz%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4 ALIGN=MIDDLE  ALT=\"c=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for z\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"z+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"z+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-3 ALIGN=MIDDLE  ALT=\"b=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-4 ALIGN=MIDDLE  ALT=\"c=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+sqrt%28+9-4%281%29%28-4%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+sqrt%28+9-4%281%29%28-4%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+sqrt%28+9--16+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+sqrt%28+9--16+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%28-4%29 ALIGN=MIDDLE  ALT=\"4%281%29%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289--16%29 ALIGN=MIDDLE  ALT=\"sqrt%289--16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%2B16%29 ALIGN=MIDDLE  ALT=\"sqrt%289%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B-+5%29%2F%282%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B-+5%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+%2B+5%29%2F%282%29 ALIGN=MIDDLE  ALT=\"z+=+%283+%2B+5%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%283+-+5%29%2F%282%29 ALIGN=MIDDLE  ALT=\"z+=+%283+-+5%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%288%29%2F%282%29 ALIGN=MIDDLE  ALT=\"z+=+%288%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=++%28-2%29%2F%282%29 ALIGN=MIDDLE  ALT=\"z+=++%28-2%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+4 ALIGN=MIDDLE  ALT=\"z+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-1 ALIGN=MIDDLE  ALT=\"z+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "----------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+4 ALIGN=MIDDLE  ALT=\"z+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29+=+4 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%5E%28-2%29 ALIGN=MIDDLE  ALT=\"z=x%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E2+=+4 ALIGN=MIDDLE  ALT=\"1%2Fx%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the left side with a positive exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=4x%5E2 ALIGN=MIDDLE  ALT=\"1=4x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4 and rearrange the equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%281%2F4%29 ALIGN=MIDDLE  ALT=\"x=sqrt%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%281%2F4%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%281%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides (don't forget the plus/minus)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the first two solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+-1 ALIGN=MIDDLE  ALT=\"z+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the second solution\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28-2%29+=+-1 ALIGN=MIDDLE  ALT=\"x%5E%28-2%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=x%5E%28-2%29 ALIGN=MIDDLE  ALT=\"z=x%5E%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E2+=+-1 ALIGN=MIDDLE  ALT=\"1%2Fx%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite the left side with a positive exponent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=-x%5E2 ALIGN=MIDDLE  ALT=\"1=-x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-1 ALIGN=MIDDLE  ALT=\"x%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by -1 and rearrange the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides (don't forget the plus/minus)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=i ALIGN=MIDDLE  ALT=\"x=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-i ALIGN=MIDDLE  ALT=\"x=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify (note: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the next two solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=i ALIGN=MIDDLE  ALT=\"x=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-i ALIGN=MIDDLE  ALT=\"x=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F2 ALIGN=MIDDLE  ALT=\"x=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=i ALIGN=MIDDLE  ALT=\"x=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-i ALIGN=MIDDLE  ALT=\"x=-i\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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