document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=493431>Question 493431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find all solutions of the equation...<BR>\n" );
document.write( "27x^3-512=0<BR>\n" );
document.write( "i know i have to get the cube or something like that<BR>\n" );
document.write( "or the GCF? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335510 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=335510\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27x%5E3-512=0 ALIGN=MIDDLE  ALT=\"27x%5E3-512=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "First, move the -512 to the other side of the equation by adding +512 to both sides as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27x%5E3-512%2B512=%2B512 ALIGN=MIDDLE  ALT=\"27x%5E3-512%2B512=%2B512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side the -512 and the +512 total zero. Therefore, you are left with the following equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27x%5E3+=512 ALIGN=MIDDLE  ALT=\"27x%5E3+=512\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > by dividing both sides by 27 and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+512%2F27 ALIGN=MIDDLE  ALT=\"x%5E3+=+512%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now note that 512 is equal to 8 cubed. Also note that 27 is equal to 3 cubed. You can verify these two statements by using a calculator to first multiply 8 times 8 times 8 to get 512. Then use it to multiply 3 times 3 times 3 and you get 27. So by substituting 8 cubed for 512 and 3 cubed for 27, you can write the equation as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+8%5E3%2F3%5E3 ALIGN=MIDDLE  ALT=\"x%5E3+=+8%5E3%2F3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "By the power rule of exponents you can furthermore write the right side of this equation as shown:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+%288%2F3%29%5E3 ALIGN=MIDDLE  ALT=\"x%5E3+=+%288%2F3%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now solve for x by taking the cube root of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288%2F3%29 ALIGN=MIDDLE  ALT=\"x+=+%288%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which simplifies to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%262%2F3 ALIGN=MIDDLE  ALT=\"x+=+2%262%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can check this answer by returning to the equation that you were originally given and substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3 ALIGN=MIDDLE  ALT=\"8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > for x. You should then see that:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%288%2F3%29%5E3+-+512+=+0 ALIGN=MIDDLE  ALT=\"27%288%2F3%29%5E3+-+512+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "becomes (after cubing the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F3 ALIGN=MIDDLE  ALT=\"8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >):<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27%2A%28512%2F27%29-512+=+0 ALIGN=MIDDLE  ALT=\"27%2A%28512%2F27%29-512+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and by cancelling the 27 in the numerator with the 27 in the denominator, this equation reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=512+-+512+=+0 ALIGN=MIDDLE  ALT=\"512+-+512+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Since the left side does equal the right side, the answer that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+8%2F3 ALIGN=MIDDLE  ALT=\"x+=+8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct.<BR>\n" );
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document.write( "Hope this helps you to see how to do this problem.<BR>\n" );
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