document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=923715>Question 923715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions (including solutions that are not real) to the following equations:\r<BR>\n" );
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document.write( "x2 – 144 = 0<BR>\n" );
document.write( "x4 – 81 = 0<BR>\n" );
document.write( "x3 – 27 = 0<BR>\n" );
document.write( "z3 + 8 = 0<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560475 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=560475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-144+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-144+=+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%5E2+-12%5E2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-12%5E2+=+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=%28x-12%29%28x%2B12%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-12%29%28x%2B12%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-12%29=+0 ALIGN=MIDDLE  ALT=\"%28x-12%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=12%29 ALIGN=MIDDLE  ALT=\"highlight%28x=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B12%29=+0 ALIGN=MIDDLE  ALT=\"%28x%2B12%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-12%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-81+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+-81+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-3%5E4+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+-3%5E4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2+-%283%5E2%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2+-%283%5E2%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29-%283%5E2%29%28x%5E2%29%2B%283%5E2%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2%29-%283%5E2%29%28x%5E2%29%2B%283%5E2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x+%2B3%29%28x-3i%29%28x%2B3i%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x+%2B3%29%28x-3i%29%28x%2B3i%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "solutions:<BR>\n" );
document.write( "real:<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29=+0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "complex:<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3i%29=+0 ALIGN=MIDDLE  ALT=\"%28x-3i%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3i%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3i%29=+0 ALIGN=MIDDLE  ALT=\"%28x%2B3i%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-3i%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-3i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-27+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-27+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-3%5E3+=+0 ALIGN=MIDDLE  ALT=\"x%5E3+-3%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%5E2%2B3x%2B9%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%5E2%2B3x%2B9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29=0 ALIGN=MIDDLE  ALT=\"%28x-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28x%5E2%2B3x%2B9%29+=+0 ALIGN=MIDDLE  ALT=\"+%28x%5E2%2B3x%2B9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > use quadratic formula:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A9+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+9-36+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+9-36+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+sqrt%28+-25+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+sqrt%28+-25+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B-+5i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B-+5i%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "complex solutions:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+%2B+5i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+%2B+5i%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+-3%2F2+%2B+5i%2F2+%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+-3%2F2+%2B+5i%2F2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3+-+5i%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%28-3+-+5i%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+-3%2F2+-+5i%2F2%29+ ALIGN=MIDDLE  ALT=\"highlight%28x+=+-3%2F2+-+5i%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+%2B+8+=+0 ALIGN=MIDDLE  ALT=\"z%5E3+%2B+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+%2B+2%5E3+=+0 ALIGN=MIDDLE  ALT=\"z%5E3+%2B+2%5E3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z%2B2%29+%28z%5E2-2z%2B4%29+=+0 ALIGN=MIDDLE  ALT=\"%28z%2B2%29+%28z%5E2-2z%2B4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "one solution: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28z%5E2-2z%2B4%29=+0 ALIGN=MIDDLE  ALT=\"+%28z%5E2-2z%2B4%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > use quadratic formula:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"z+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"z=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%282+%2B-+sqrt%284-16+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"z+=+%282+%2B-+sqrt%284-16+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%282+%2B-+sqrt%28+-12+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"z+=+%282+%2B-+sqrt%28+-12+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%282+%2B-+sqrt%28+-4%2A3+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"z+=+%282+%2B-+sqrt%28+-4%2A3+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%282+%2B-+2i%2Asqrt%283%29%29%2F2+ ALIGN=MIDDLE  ALT=\"z+=+%282+%2B-+2i%2Asqrt%283%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "complex solutions:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+%2B+2i%2Asqrt%283%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%282+%2B+2i%2Asqrt%283%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F2+%2B+2i%2Asqrt%283%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+2%2F2+%2B+2i%2Asqrt%283%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+1%2B+sqrt%283%29%2Ai%29+ ALIGN=MIDDLE  ALT=\"highlight%28x+=+1%2B+sqrt%283%29%2Ai%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%282+-2i%2Asqrt%283%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%282+-2i%2Asqrt%283%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2F2+-+2i%2Asqrt%283%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+2%2F2+-+2i%2Asqrt%283%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+1-+sqrt%283%29%2Ai%29+ ALIGN=MIDDLE  ALT=\"highlight%28x+=+1-+sqrt%283%29%2Ai%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );