document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189607>Question 189607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this? I have to solve for all roots. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-5x%5E2-24=0 ALIGN=MIDDLE  ALT=\"x%5E4-5x%5E2-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142289 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=142289\">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=x%5E4-5x%5E2-24+=+0 ALIGN=MIDDLE  ALT=\"x%5E4-5x%5E2-24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "You can write this as a quadratic equation with a temporary change of variable, thus...<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+=+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E4+=+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then you substitute...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2-5y-24+=+0 ALIGN=MIDDLE  ALT=\"y%5E2-5y-24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor this...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-8%29%28y%2B3%29+=+0 ALIGN=MIDDLE  ALT=\"%28y-8%29%28y%2B3%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=y-8+=+0 ALIGN=MIDDLE  ALT=\"y-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B3+=+0 ALIGN=MIDDLE  ALT=\"y%2B3+=+0\"   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=y+=+8 ALIGN=MIDDLE  ALT=\"y+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3 ALIGN=MIDDLE  ALT=\"y+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now substitue back <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2 ALIGN=MIDDLE  ALT=\"y+=+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so you have...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+8 ALIGN=MIDDLE  ALT=\"x%5E2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-3 ALIGN=MIDDLE  ALT=\"x%5E2+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%288%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%288%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28-3%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-3%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The roots are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%288%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%288%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+=+-sqrt%288%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%288%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+=+sqrt%283%29i ALIGN=MIDDLE  ALT=\"x+=+sqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%283%29i ALIGN=MIDDLE  ALT=\"x+=+-sqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: <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;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );