document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=84579>Question 84579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve by making appropriate substitution.\r<BR>\n" );
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document.write( "x^4 - 14x^2 - 32 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #60960 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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/cgi-bin/show-face.mpl?user=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=60960\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The method you are asked to use for this problem is the method of substitution.  You should begin by noticing that in this equation, if you let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E2 ALIGN=MIDDLE  ALT=\"u=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+=+%28x%5E2%29%5E2=+x%5E4 ALIGN=MIDDLE  ALT=\"u%5E2+=+%28x%5E2%29%5E2=+x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, make these substitutions and you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-+14x%5E2+-+32+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+-+14x%5E2+-+32+=+0\"   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+-+14u+-+32+=+0+ ALIGN=MIDDLE  ALT=\"u%5E2+-+14u+-+32+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This factors into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28u-16%29%28u%2B2%29+=+0 ALIGN=MIDDLE  ALT=\"%28u-16%29%28u%2B2%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=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=+-2 ALIGN=MIDDLE  ALT=\"u=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Don't stop here!  You must still solve for the original variable which is x.  Substitute these values of u back into the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=x%5E2 ALIGN=MIDDLE  ALT=\"u=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=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=+-2 ALIGN=MIDDLE  ALT=\"u=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=+-2 ALIGN=MIDDLE  ALT=\"x%5E2=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, are you supposed to give REAL solutions, or are you supposed to also include imaginary (complex) solutions?  IF COMPLEX solutions are allowed, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16 ALIGN=MIDDLE  ALT=\"x%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=+-2 ALIGN=MIDDLE  ALT=\"x%5E2=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+0%2B-sqrt%2816%29 ALIGN=MIDDLE  ALT=\"x=+0%2B-sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+0%2B-sqrt%28-2%29+ ALIGN=MIDDLE  ALT=\"x=+0%2B-sqrt%28-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+4 ALIGN=MIDDLE  ALT=\"x=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+0%2B-i%2Asqrt%282%29+ ALIGN=MIDDLE  ALT=\"x=+0%2B-i%2Asqrt%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you are finding ONLY REAL solutions, then the answer is only x=4 or x=-4.\r<BR>\n" );
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document.write( "Note:  You don't really need the 0 in the answers above.  It's just that in the algebra.com format, you can't write this + or - notation without using the 0!  Sorry about that.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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