document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263095>Question 263095</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all real solutions of the equation. List solutions in increasing order. \r<BR>\n" );
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document.write( "2(x^-4) - 10(x^-2) + 2 = 0\r<BR>\n" );
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document.write( "Have tried to simplify and eliminate but must be missing something because I can't get anything to equal 0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193815 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=193815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we are given the following equation<BR>\n" );
document.write( "(i) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E-4%29+-+10%28x%5E-2%29+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"2%28x%5E-4%29+-+10%28x%5E-2%29+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 1 - multiply all terms by x^4 to get<BR>\n" );
document.write( "(ii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+-10x%5E2+-+2x%5E4+=+0 ALIGN=MIDDLE  ALT=\"2+-10x%5E2+-+2x%5E4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "rewrite in descending order; divide by -2 to get<BR>\n" );
document.write( "(iii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2B5x%5E2+-1+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+%2B5x%5E2+-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let x^2 = U and we get<BR>\n" );
document.write( "(iv) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U%5E2+%2B5U+-1+=+0 ALIGN=MIDDLE  ALT=\"U%5E2+%2B5U+-1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "factor using the quadratic to get<BR>\n" );
document.write( "(v) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+%28-5+%2B-+sqrt%2825-4%2A1%2A%28-1%29%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"U+=+%28-5+%2B-+sqrt%2825-4%2A1%2A%28-1%29%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "(vi) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U+=+%28-5%2B-+sqrt%2829%29%29%2F2 ALIGN=MIDDLE  ALT=\"U+=+%28-5%2B-+sqrt%2829%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now replace U with x^2 to get<BR>\n" );
document.write( "(vii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+%28-5%2B-+sqrt%2829%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5E2+=+%28-5%2B-+sqrt%2829%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "taking a square root gives us<BR>\n" );
document.write( "(viii) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B-sqrt%28%28-5%2B-sqrt%2829%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"x+=+%2B-sqrt%28%28-5%2B-sqrt%2829%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );