document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260277>Question 260277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve this equation: x^3+729=0\r<BR>\n" );
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document.write( "I know this much:  1st solution is -9<BR>\n" );
document.write( "(x+9)^3=0<BR>\n" );
document.write( "(x+9)[x^2-9x+81]\r<BR>\n" );
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document.write( "This is where I'm stuck..When I use the quadratic formula I get\r<BR>\n" );
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document.write( "9 +/-square root of 243 over 2\r<BR>\n" );
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document.write( "Now what?    The answer is 9 +9i 'square root' of 3 over 2.  How do you get that? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191712 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=191712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the original question:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B729=0+ ALIGN=MIDDLE  ALT=\"x%5E3%2B729=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we can express this as the sum of cubes, but first write them both as powers of 3, as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B9%5E3+=+0 ALIGN=MIDDLE  ALT=\"x%5E3%2B9%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%29%28x%5E2-9x%2B81%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%28x%5E2-9x%2B81%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "next set each part =0 and solve.<BR>\n" );
document.write( "x+9 = 0<BR>\n" );
document.write( "x = -9<BR>\n" );
document.write( "--<BR>\n" );
document.write( "x^2-9x+81= 0 <BR>\n" );
document.write( "by quadratic, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%289+%2B-+sqrt%28+81-4%2A1%2A81+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%289+%2B-+sqrt%28+81-4%2A1%2A81+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%289+%2B-+sqrt%2881-324%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%289+%2B-+sqrt%2881-324%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%289+%2B-+sqrt%28-243+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%289+%2B-+sqrt%28-243+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which will give us imaginary roots as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%289+%2B-+9%2Aisqrt%283%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%289+%2B-+9%2Aisqrt%283%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "we have three roots<BR>\n" );
document.write( "x = -9<BR>\n" );
document.write( "x = (9+9isqrt(3))/2<BR>\n" );
document.write( "x = (9-9isqrt(3))/2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );