document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=352103>Question 352103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello!<BR>\n" );
document.write( "My problem is finding all real solutions with the following equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29-5x%5E%282%2F3%29%2B6 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29-5x%5E%282%2F3%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I put 6 on the other side so it turns into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29-5x%5E%282%2F3%29=-6 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29-5x%5E%282%2F3%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can't combine the two terms so I ended up subtracting -5x^(2/3) from both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29=5x%5E%282%2F3%29-6 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29=5x%5E%282%2F3%29-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then I will take the power 3/4th to both sides so X on the left is by itself.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%285x%5E%282%2F3%29%29%5E%283%2F4%29-6%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"x=%285x%5E%282%2F3%29%29%5E%283%2F4%29-6%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which will simplify to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E%281%2F4%29%2Ax%5E%281%2F2%29-126%5E%281%2F4%29=X ALIGN=MIDDLE  ALT=\"125%5E%281%2F4%29%2Ax%5E%281%2F2%29-126%5E%281%2F4%29=X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is where I get stuck.<BR>\n" );
document.write( "I have a feeling I screwed up somewhere.<BR>\n" );
document.write( "Can you please help me?<BR>\n" );
document.write( "Thank you.<BR>\n" );
document.write( "-Kayte. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #251566 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=251566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> My problem is finding all real solutions with the following equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29-5x%5E%282%2F3%29%2B6 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29-5x%5E%282%2F3%29%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I put 6 on the other side so it turns into<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29-5x%5E%282%2F3%29=-6 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29-5x%5E%282%2F3%29=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can't combine the two terms so I ended up subtracting -5x^(2/3) from both sides to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%284%2F3%29=5x%5E%282%2F3%29-6 ALIGN=MIDDLE  ALT=\"x%5E%284%2F3%29=5x%5E%282%2F3%29-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then I will take the power 3/4th to both sides so X on the left is by itself.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%285x%5E%282%2F3%29%29%5E%283%2F4%29-6%5E%283%2F4%29 ALIGN=MIDDLE  ALT=\"x=%285x%5E%282%2F3%29%29%5E%283%2F4%29-6%5E%283%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Which will simplify to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125%5E%281%2F4%29%2Ax%5E%281%2F2%29-126%5E%281%2F4%29=X ALIGN=MIDDLE  ALT=\"125%5E%281%2F4%29%2Ax%5E%281%2F2%29-126%5E%281%2F4%29=X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "============================================<BR>\n" );
document.write( "x^(4/3)-5x^(2/3)+6}<BR>\n" );
document.write( "Your problem is a quadratic with variable x^(2/3).<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "It can be written as:<BR>\n" );
document.write( "[x^(2/3)]^2 - 5[x^(2/3)] +6 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "It factors as:<BR>\n" );
document.write( "[x^(2/3)-3][x^(2/3)-2] = 0<BR>\n" );
document.write( "Then:<BR>\n" );
document.write( "x^(2/3) = 3 or x^(2/3) = 2<BR>\n" );
document.write( "x = 3^(3/2) or x = 1^(3/2)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = 3sqrt(3) or x = 1<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );