document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1004969>Question 1004969</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The problem says to find all the solutions of the equation with the given value of x as a solution... I am so lost\r<BR>\n" );
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document.write( "x^3+3x^2+16x-20=0<BR>\n" );
document.write( "x=-2+4i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621337 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=621337\">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%5E3%2B3x%5E2%2B16x-20=0 ALIGN=MIDDLE  ALT=\"x%5E3%2B3x%5E2%2B16x-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using zero product theorem, we can write the 3rd degree function as \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE  ALT=\"%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-2%2B4i ALIGN=MIDDLE  ALT=\"x%5B1%5D=-2%2B4i\"   DISABLED_style= \"max-width:90%; height:auto;\" >...if you have this root, you have to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-2-4i ALIGN=MIDDLE  ALT=\"x%5B2%5D=-2-4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > too (complex roots always in pairs)\r<BR>\n" );
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document.write( "then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-2%2B4i%29%29%28x-%28-2-4i%29%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE  ALT=\"%28x-%28-2%2B4i%29%29%28x-%28-2-4i%29%29%28x-x%5B3%5D%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=%28x%2B2-4i%29%28x%2B2%2B4i%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2-4i%29%28x%2B2%2B4i%29%28x-x%5B3%5D%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=%28x%5E2%2B2x%2B4xi%2B2x%2B4%2B8i-4xi-8i-16i%5E2%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2x%2B4xi%2B2x%2B4%2B8i-4xi-8i-16i%5E2%29%28x-x%5B3%5D%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=%28x%5E2%2B2x%2Bcross%284xi%29%2B2x%2B4%2Bcross%288i%29-cross%284xi%29-cross%288i%29-16%28-1%29%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE   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%5E2%2B2x%2B2x%2B4%2B16%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B2x%2B2x%2B4%2B16%29%28x-x%5B3%5D%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=%28x%5E2%2B4x%2B20%29%28x-x%5B3%5D%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2B20%29%28x-x%5B3%5D%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B3x%5E2%2B16x-20=%28x%5E2%2B4x%2B20%29%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B3x%5E2%2B16x-20=%28x%5E2%2B4x%2B20%29%28x-x%5B3%5D%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=%28x%5E3%2B3x%5E2%2B16x-20%29%2F%28x%5E2%2B4x%2B20%29=%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B3x%5E2%2B16x-20%29%2F%28x%5E2%2B4x%2B20%29=%28x-x%5B3%5D%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=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2B20%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >|(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B3x%5E2%2B16x-20 ALIGN=MIDDLE  ALT=\"x%5E3%2B3x%5E2%2B16x-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "-------------------<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B4x%5E2%2B20x ALIGN=MIDDLE  ALT=\"x%5E3%2B4x%5E2%2B20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >........subtract<BR>\n" );
document.write( "--------------------<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0-x%5E2-4x ALIGN=MIDDLE  ALT=\"0-x%5E2-4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........bring down <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20 ALIGN=MIDDLE  ALT=\"-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-4x-20 ALIGN=MIDDLE  ALT=\"-x%5E2-4x-20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2-4x-20 ALIGN=MIDDLE  ALT=\"-x%5E2-4x-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >...subtract<BR>\n" );
document.write( "-------------------...........<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......reminder\r<BR>\n" );
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document.write( "so, third product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-x%5B3%5D%29=x-1 ALIGN=MIDDLE  ALT=\"%28x-x%5B3%5D%29=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=1 ALIGN=MIDDLE  ALT=\"x%5B3%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and your equation is factored as following:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2-4i%29%28x%2B2%2B4i%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B2-4i%29%28x%2B2%2B4i%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and, roots are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-2%2B4i ALIGN=MIDDLE  ALT=\"x%5B1%5D=-2%2B4i\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=-2-4i ALIGN=MIDDLE  ALT=\"x%5B2%5D=-2-4i\"   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%5B3%5D=1 ALIGN=MIDDLE  ALT=\"x%5B3%5D=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );