document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=353894>Question 353894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a hard exponent quadratic question.\r<BR>\n" );
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document.write( "5x^2/3 + 2x^4/3 -13 =0\r<BR>\n" );
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document.write( "My first inclination was to rearrange the terms to...\r<BR>\n" );
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document.write( "2x^4/3 + 5x^2/3 -13 =0\r<BR>\n" );
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document.write( "This puts it in the right order for substitution / y= x^2/3\r<BR>\n" );
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document.write( "Thus... 2y^2 + 5y -13 =0\r<BR>\n" );
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document.write( "This is where I'm stuck. I don't know how to unfold the answer with the unusual powers.\r<BR>\n" );
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document.write( "Thanks for your help.<BR>\n" );
document.write( "Neil </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #252979 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=252979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 5x^2/3 + 2x^4/3 -13 =0 <BR>\n" );
document.write( "My first inclination was to rearrange the terms to... <BR>\n" );
document.write( "2x^4/3 + 5x^2/3 -13 =0 <BR>\n" );
document.write( "This puts it in the right order for substitution / y= x^2/3 <BR>\n" );
document.write( "Thus... 2y^2 + 5y -13 =0<BR>\n" );
document.write( "This is where I'm stuck. I don't know how to unfold the answer with the unusual powers. <BR>\n" );
document.write( "Thanks for your help.<BR>\n" );
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document.write( "Solve your equation for y:<BR>\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=2x%5E2%2B5x%2B-13+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x%2B-13+=+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=%285%29%5E2-4%2A2%2A-13=129 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A2%2A-13=129\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=129 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+=+%28-5%2B-sqrt%28+129+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+129+%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-%285%29%2Bsqrt%28+129+%29%29%2F2%5C2+=+1.58945417290014 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%285%29%2Bsqrt%28+129+%29%29%2F2%5C2+=+1.58945417290014\"   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-%285%29-sqrt%28+129+%29%29%2F2%5C2+=+-4.08945417290014 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%285%29-sqrt%28+129+%29%29%2F2%5C2+=+-4.08945417290014\"   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=2x%5E2%2B5x%2B-13 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x%2B-13\"   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=2x%5E2%2B5x%2B-13+=+%28x-1.58945417290014%29%2A%28x--4.08945417290014%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B5x%2B-13+=+%28x-1.58945417290014%29%2A%28x--4.08945417290014%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.58945417290014, -4.08945417290014.\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+2%2Ax%5E2%2B5%2Ax%2B-13+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-13+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "y = -5/4 ± sqrt(129)/4<BR>\n" );
document.write( "x^(2/3) = -5/4 ± sqrt(129)/4<BR>\n" );
document.write( "It's messy, but it's just arithmetic from here.<BR>\n" );
document.write( "Cube both sides:<BR>\n" );
document.write( "x^(2/3) = -5/4 + sqrt(129)/4<BR>\n" );
document.write( "x^2 = (1/16)*(-515 + 51sqrt(129))<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B+%281%2F4%29%2Asqrt%28-515+%2B+51sqrt%28129%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2B+%281%2F4%29%2Asqrt%28-515+%2B+51sqrt%28129%29%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+=+-+%281%2F4%29%2Asqrt%28-515+%2B+51sqrt%28129%29%29 ALIGN=MIDDLE  ALT=\"x+=+-+%281%2F4%29%2Asqrt%28-515+%2B+51sqrt%28129%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Can you do rest?<BR>\n" );
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