document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=717596>Question 717596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me solve this polynomial equation algebraically:<BR>\n" );
document.write( "(12x^4) - (3x^2) - 54 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #440494 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=440494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Divide left and right members by 3.  Substitute for x^2 as a different single variable and solve for that variable; and then reverse the subsitution to continue solving for x.\r<BR>\n" );
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document.write( "Your equation is the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E4-x%5E2-18=0 ALIGN=MIDDLE  ALT=\"4x%5E4-x%5E2-18=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "You could ignore the substitution for x^2 suggestion and go along with x^2 as the variable, and THEN continue on for x. The simpler equation on the left side is factorable, so you now have  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284x%5E2-9%29%28x%5E2%2B2%29=0 ALIGN=MIDDLE  ALT=\"%284x%5E2-9%29%28x%5E2%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "For x^2+2=0, no real solution.  Complex solution yes. No real one.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2Asqrt%282%29=x ALIGN=MIDDLE  ALT=\"i%2Asqrt%282%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-i%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"-i%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "For 4x^2-9=0, 4x^2=9, x^2=9/4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B3%2F2 ALIGN=MIDDLE  ALT=\"x=%2B3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3%2F2 ALIGN=MIDDLE  ALT=\"x=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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