document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=789099>Question 789099</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.) Find the solutions of the equation.<BR>\n" );
document.write( "    I already subuted u for x^(2/3) then i got a quadratic equation 3u^2 + 5u -     2=0 and i got u = 1/3 and -2 and i have to sub something back but I do not know what to do now after i got those two answers for u?\r<BR>\n" );
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document.write( "3x^(4/3) + 5x^(2/3) - 2=0 \r<BR>\n" );
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document.write( "Can someone please help me on this problem and go step by step with this equtaion for me? THANK YOU!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478721 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=478721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+x%5E%282%2F3%29%5E%22%22 ALIGN=MIDDLE  ALT=\"u+=+x%5E%282%2F3%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So because the first solution for 'u' is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u+=+1%2F3 ALIGN=MIDDLE  ALT=\"u+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%22%22%2B-sqrt%281%2F27%29 ALIGN=MIDDLE  ALT=\"x+=+%22%22%2B-sqrt%281%2F27%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=x+=+sqrt%281%2F27%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%281%2F27%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%281%2F27%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%281%2F27%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=x+=+sqrt%281%29%2Fsqrt%2827%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%281%29%2Fsqrt%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%281%29%2Fsqrt%2827%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%281%29%2Fsqrt%2827%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=x+=+1%2Fsqrt%2827%29 ALIGN=MIDDLE  ALT=\"x+=+1%2Fsqrt%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2Fsqrt%2827%29 ALIGN=MIDDLE  ALT=\"x+=+-1%2Fsqrt%2827%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=x+=+1%2Fsqrt%289%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+1%2Fsqrt%289%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2Fsqrt%289%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+-1%2Fsqrt%289%2A3%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=x+=+1%2F%28sqrt%289%29%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+1%2F%28sqrt%289%29%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F%28sqrt%289%29%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+-1%2F%28sqrt%289%29%2Asqrt%283%29%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=x+=+1%2F%283%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+1%2F%283%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%2F%283%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+-1%2F%283%2Asqrt%283%29%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=x+=+%281%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%281%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"x+=+-%281%2Asqrt%283%29%29%2F%283%2Asqrt%283%29%2Asqrt%283%29%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=x+=+%28sqrt%283%29%29%2F%283%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+%28sqrt%283%29%29%2F%283%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28sqrt%283%29%29%2F%283%2A3%29 ALIGN=MIDDLE  ALT=\"x+=+-%28sqrt%283%29%29%2F%283%2A3%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=x+=+%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+-%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Now if <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;\" >, then...\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%28-8%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-sqrt%28-8%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-8%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=x+=+sqrt%28-1%2A4%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-1%2A4%2A2%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%2A4%2A2%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-1%2A4%2A2%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=x+=+sqrt%28-1%29%2Asqrt%284%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%28-1%29%2Asqrt%284%29%2Asqrt%282%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%2Asqrt%284%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+-sqrt%28-1%29%2Asqrt%284%29%2Asqrt%282%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=x+=+i%2A2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+i%2A2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-i%2A2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+-i%2A2%2Asqrt%282%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=x+=+2i%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+2i%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2i%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"x+=+-2i%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since these solutions are complex and not real, we can ignore them.\r<BR>\n" );
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document.write( "So the two *possible* real numbered solutions are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+-%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It turns out that when you plug each back into the original equation, only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > works while <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+-%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > makes the original equation false.\r<BR>\n" );
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document.write( "Therefore, the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28sqrt%283%29%29%2F%289%29 ALIGN=MIDDLE  ALT=\"x+=+%28sqrt%283%29%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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