document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=210762>Question 210762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (6x-5)^2/3 = x^1/3<BR>\n" );
document.write( "I have no idea what to do. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159222 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><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=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159222\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK.. first step is not to panic :-)<BR>\n" );
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document.write( "Next step is remember some laws about exponents. Namely that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%282%2F3%29=%28x%5E2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"x%5E%282%2F3%29=%28x%5E2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can apply that to the left side of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x-5%29%5E%282%2F3%29+=+x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%286x-5%29%5E%282%2F3%29+=+x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%286x-5%29%5E2%29%5E%281%2F3%29=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28%286x-5%29%5E2%29%5E%281%2F3%29=x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now square that binomial:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2836x%5E2-60x%2B25%29%5E%281%2F3%29=x%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%2836x%5E2-60x%2B25%29%5E%281%2F3%29=x%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cube both sides of the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2-60x%2B25=x ALIGN=MIDDLE  ALT=\"36x%5E2-60x%2B25=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equate to zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2-61x%2B25=0 ALIGN=MIDDLE  ALT=\"36x%5E2-61x%2B25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is looking much more manageable now. just apply the quadratic formula to this and you are done:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2%2B-61x%2B25+=+0 ALIGN=MIDDLE  ALT=\"36x%5E2%2B-61x%2B25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-61%29%5E2-4%2A36%2A25=121 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-61%29%5E2-4%2A36%2A25=121\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=121 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--61%2B-sqrt%28+121+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--61%2B-sqrt%28+121+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-61%29%2Bsqrt%28+121+%29%29%2F2%5C36+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-61%29%2Bsqrt%28+121+%29%29%2F2%5C36+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-61%29-sqrt%28+121+%29%29%2F2%5C36+=+0.694444444444444 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-61%29-sqrt%28+121+%29%29%2F2%5C36+=+0.694444444444444\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2%2B-61x%2B25 ALIGN=MIDDLE  ALT=\"36x%5E2%2B-61x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36x%5E2%2B-61x%2B25+=+36%28x-1%29%2A%28x-0.694444444444444%29 ALIGN=MIDDLE  ALT=\"36x%5E2%2B-61x%2B25+=+36%28x-1%29%2A%28x-0.694444444444444%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1, 0.694444444444444.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+36%2Ax%5E2%2B-61%2Ax%2B25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+36%2Ax%5E2%2B-61%2Ax%2B25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "===================<BR>\n" );
document.write( "Good Luck,<BR>\n" );
document.write( "tutor_paul@yahoo.com </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );