document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=660769>Question 660769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%3E+0+ ALIGN=MIDDLE  ALT=\"+a+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > show that the solution set of the inequality <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%3E+a+ ALIGN=MIDDLE  ALT=\"+x%5E2+%3E+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > consists of all numbers x for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+-+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3C+-+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3E+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "I figured it out all the way to the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x+%2B+sqrt%28a%29%29%28x+-+sqrt%28a%29%29+%3E+0+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+sqrt%28a%29%29%28x+-+sqrt%28a%29%29+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from here ,when I try to solve for x by setting each factor as greater than 0, I get the opposite result of what I need, i.e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+-+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3E+-+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+-+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3C+-+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and I don't know why. Thanks so much again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #411356 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=411356\">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=+%28x+%2B+sqrt%28a%29%29%28x+-+sqrt%28a%29%29+%3E+0+ ALIGN=MIDDLE  ALT=\"+%28x+%2B+sqrt%28a%29%29%28x+-+sqrt%28a%29%29+%3E+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "Just looking at the signs of the 2 factors,<BR>\n" );
document.write( "Neither factor can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These 2 cases work:<BR>\n" );
document.write( "(+) * (+) >0<BR>\n" );
document.write( "( - ) * ( - ) > 0<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "These don't work:<BR>\n" );
document.write( "(+) * (-)<BR>\n" );
document.write( "( - ) * (+)<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "The 1st case:<BR>\n" );
document.write( "(+) * (+) >0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+sqrt%28a%29+%3E+0+ ALIGN=MIDDLE  ALT=\"+x+%2B+sqrt%28a%29+%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=+x+%3E+-sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3E+-sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+sqrt%28a%29+%3E+0+ ALIGN=MIDDLE  ALT=\"+x+-+sqrt%28a%29+%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=+x+%3E+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3E+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Both of these have to be true. They are only<BR>\n" );
document.write( "true if the 1st is true, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+-sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3E+-sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "must hold<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "The 2nd case<BR>\n" );
document.write( "(-)*(-) >0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%2B+sqrt%28a%29+%3C+0+ ALIGN=MIDDLE  ALT=\"+x+%2B+sqrt%28a%29+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+-sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3C+-sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+sqrt%28a%29+%3C+0+ ALIGN=MIDDLE  ALT=\"+x+-+sqrt%28a%29+%3C+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3C+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "Both of these have to be true. They are only true<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+-sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3C+-sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3C+-sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3C+-sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+%3E+sqrt%28a%29+ ALIGN=MIDDLE  ALT=\"+x+%3E+sqrt%28a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since either of the 2 cases works\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );