document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189584>Question 189584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve this? I'm supposed to solve for all roots but I'm not sure how. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B27=0 ALIGN=MIDDLE  ALT=\"8x%5E3%2B27=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142259 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=142259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, we need to factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B27 ALIGN=MIDDLE  ALT=\"8x%5E3%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B27 ALIGN=MIDDLE  ALT=\"8x%5E3%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the left side of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E3%2B%283%29%5E3 ALIGN=MIDDLE  ALT=\"%282x%29%5E3%2B%283%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3 ALIGN=MIDDLE  ALT=\"8x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%5E3 ALIGN=MIDDLE  ALT=\"%282x%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27 ALIGN=MIDDLE  ALT=\"27\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29%5E3 ALIGN=MIDDLE  ALT=\"%283%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%28%282x%29%5E2-%282x%29%283%29%2B%283%29%5E2%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%28%282x%29%5E2-%282x%29%283%29%2B%283%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor by using the sum of cubes formula. Remember the <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/specfact2.htm\">sum of cubes formula</a> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29 ALIGN=MIDDLE  ALT=\"A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%284x%5E2-6x%2B9%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%284x%5E2-6x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B27 ALIGN=MIDDLE  ALT=\"8x%5E3%2B27\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%284x%5E2-6x%2B9%29 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%284x%5E2-6x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B27=%282x%2B3%29%284x%5E2-6x%2B9%29 ALIGN=MIDDLE  ALT=\"8x%5E3%2B27=%282x%2B3%29%284x%5E2-6x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E3%2B27=0 ALIGN=MIDDLE  ALT=\"8x%5E3%2B27=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%284x%5E2-6x%2B9%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%284x%5E2-6x%2B9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B3%29%284x%5E2-6x%2B9%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B3%29%284x%5E2-6x%2B9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the factored equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=0 ALIGN=MIDDLE  ALT=\"2x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-6x%2B9=0 ALIGN=MIDDLE  ALT=\"4x%5E2-6x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set each factor equal to zero\r<BR>\n" );
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document.write( "Let's solve the first equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=0 ALIGN=MIDDLE  ALT=\"2x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B3=0 ALIGN=MIDDLE  ALT=\"2x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the first equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-3 ALIGN=MIDDLE  ALT=\"2x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 3 from both sides.\r<BR>\n" );
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document.write( "<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;\" > Divide both sides by 2.\r<BR>\n" );
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document.write( "So the first answer is <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;\" >\r<BR>\n" );
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document.write( "Now let's solve the second equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-6x%2B9=0 ALIGN=MIDDLE  ALT=\"4x%5E2-6x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=9 ALIGN=MIDDLE  ALT=\"c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-6 ALIGN=MIDDLE  ALT=\"b=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=9 ALIGN=MIDDLE  ALT=\"c=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+36-4%284%29%289%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36-4%284%29%289%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+36-144+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+36-144+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%29%289%29 ALIGN=MIDDLE  ALT=\"4%284%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+-108+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+-108+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-108 ALIGN=MIDDLE  ALT=\"-108\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+sqrt%28+-108+%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+sqrt%28+-108+%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286+%2B-+6i%2Asqrt%283%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%286+%2B-+6i%2Asqrt%283%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286%2B6i%2Asqrt%283%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%286%2B6i%2Asqrt%283%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%286-6i%2Asqrt%283%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%286-6i%2Asqrt%283%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2B3i%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2B3i%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283-3i%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%283-3i%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the other two answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2B3i%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2B3i%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283-3i%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%283-3i%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the three solutions are <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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2B3i%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2B3i%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283-3i%2Asqrt%283%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%283-3i%2Asqrt%283%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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