document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10848>Question 10848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation in the complex number system\r<BR>\n" );
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document.write( "1.X^3 - 8 = 0<BR>\n" );
document.write( "2. X^3 + 27 = 0\r<BR>\n" );
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document.write( "my solution<BR>\n" );
document.write( "1.   X^3 - 8 = 0<BR>\n" );
document.write( "     X^3 = 8<BR>\n" );
document.write( "       X= 3root 8<BR>\n" );
document.write( "       X= +- 2<BR>\n" );
document.write( "       X= +2 , -2\r<BR>\n" );
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document.write( "2. X^3 + 27 = 0<BR>\n" );
document.write( "   x^3=27<BR>\n" );
document.write( "    X =+- 3root 27<BR>\n" );
document.write( "    X= + - 3<BR>\n" );
document.write( "    X= =3, -3\r<BR>\n" );
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document.write( "I know I'm wrong but I don't know why. kindly help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5811 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=5811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+8+=+0+ ALIGN=MIDDLE  ALT=\"x%5E3+-+8+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 8 to both sides, which you did already.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+=+8 ALIGN=MIDDLE  ALT=\"x%5E3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the cube root of both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  -2 is not a root since: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-2%29%5E3+=+%28-2%29%28-2%29%28-2%29 ALIGN=MIDDLE  ALT=\"+%28-2%29%5E3+=+%28-2%29%28-2%29%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -8\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+27+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+27+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 27 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%5E3+=+-27 ALIGN=MIDDLE  ALT=\"x%5E3+=+-27\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the cube root of 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 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "+3 is not a root since: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2B3%29%5E3+=+%28%2B3%29%28%2B3%29%28%2B3%29 ALIGN=MIDDLE  ALT=\"%28%2B3%29%5E3+=+%28%2B3%29%28%2B3%29%28%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = +27\r<BR>\n" );
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document.write( "Please ignore the above...it's wrong!\r<BR>\n" );
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document.write( "1)  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-+8+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  This is the difference of two cubes which can be factored as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+2%29%28x%5E2+%2B+2x+%2B+4%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+2%29%28x%5E2+%2B+2x+%2B+4%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=x+-+2+=+0 ALIGN=MIDDLE  ALT=\"x+-+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > One root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x++%2B+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x++%2B+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2+-+4ac%29%29%2F2a\"   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+=+%28-2%2B-sqrt%284-16%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-2%2B-sqrt%284-16%29%29%2F2\"   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+=+%28-2%2B-sqrt%28-12%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-2%2B-sqrt%28-12%29%29%2F2\"   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+=+-1%2B-sqrt%28-3%2A4%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+-1%2B-sqrt%28-3%2A4%29%2F2\"   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+=+-1%2Bsqrt%283%29i ALIGN=MIDDLE  ALT=\"x+=+-1%2Bsqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1-sqrt%283%29i ALIGN=MIDDLE  ALT=\"x+=+-1-sqrt%283%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" > The other two roots.\r<BR>\n" );
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document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2B+27+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+%2B+27+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the sum of two cubes which can be factored as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29%28x%5E2+-+3x+%2B+9%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29%28x%5E2+-+3x+%2B+9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Setting each factor = 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B+3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3 ALIGN=MIDDLE  ALT=\"x+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is one of the roots.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+3x+%2B+9+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+3x+%2B+9+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a\"   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=%283%2B-sqrt%289-36%29%29%2F2 ALIGN=MIDDLE  ALT=\"x=%283%2B-sqrt%289-36%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2F2%29%2B-sqrt%28-27%29%2F2 ALIGN=MIDDLE  ALT=\"x=%283%2F2%29%2B-sqrt%28-27%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2F2%29%2B3sqrt%283%29i%2F2 ALIGN=MIDDLE  ALT=\"x=%283%2F2%29%2B3sqrt%283%29i%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2F2%29-3sqrt%283%29i%2F2 ALIGN=MIDDLE  ALT=\"x=%283%2F2%29-3sqrt%283%29i%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > The other two roots.\r<BR>\n" );
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document.write( "These can also be written:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2F2%29%281%2Bsqrt%283%29i%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2F2%29%281%2Bsqrt%283%29i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%283%2F2%29%281-sqrt%283%29i%29 ALIGN=MIDDLE  ALT=\"x+=+%283%2F2%29%281-sqrt%283%29i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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