document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013018>Question 1013018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find four roots of the following equation:\r<BR>\n" );
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document.write( "2x^4 +5x^2 = 207\r<BR>\n" );
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document.write( "* I plugged into my calculator and only got 2 roots, x=-3 and x=3, but how do you get the rest? Thanks :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629176 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=629176\">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=2x%5E4+%2B5x%5E2+=+207 ALIGN=MIDDLE  ALT=\"2x%5E4+%2B5x%5E2+=+207\"   DISABLED_style= \"max-width:90%; height:auto;\" > write in standard form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E4%2B5x%5E2-207+=0 ALIGN=MIDDLE  ALT=\"+2x%5E4%2B5x%5E2-207+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2x%5E4%2B5x%5E2-207+=0 ALIGN=MIDDLE  ALT=\"+2x%5E4%2B5x%5E2-207+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The first term is,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4 ALIGN=MIDDLE  ALT=\"2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  its coefficient is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The middle term is,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%5E2+ ALIGN=MIDDLE  ALT=\"5x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > its coefficient is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The last term, \"the constant\", is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-207+ ALIGN=MIDDLE  ALT=\"-207+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " Multiply the coefficient of the first term by the constant  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+%28-207%29+=+-414+ ALIGN=MIDDLE  ALT=\"+2+%28-207%29+=+-414+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find two factors of  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-414 ALIGN=MIDDLE  ALT=\"-414\"   DISABLED_style= \"max-width:90%; height:auto;\" >  whose sum equals the coefficient of the middle term, which is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >: these are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18 ALIGN=MIDDLE  ALT=\"-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  Rewrite the polynomial splitting the middle term using the two factors found above,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-18 ALIGN=MIDDLE  ALT=\"-18\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23 ALIGN=MIDDLE  ALT=\"23\"   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=+2x%5E4+-+18x%5E2+%2B+23x%5E2+-+207=0 ALIGN=MIDDLE  ALT=\"+2x%5E4+-+18x%5E2+%2B+23x%5E2+-+207=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ............group first two terms together and second two terms together\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E4+-18x%5E2%29+%2B+%2823x%5E2+-207%29=0 ALIGN=MIDDLE  ALT=\"%282x%5E4+-18x%5E2%29+%2B+%2823x%5E2+-207%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=+2x%5E2%28x%5E2+-+9%29+%2B+23%28x%5E2+-9%29=0 ALIGN=MIDDLE  ALT=\"+2x%5E2%28x%5E2+-+9%29+%2B+23%28x%5E2+-9%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%5E2%2B+23%29%28x%5E2+-+9%29=0 ALIGN=MIDDLE  ALT=\"%282x%5E2%2B+23%29%28x%5E2+-+9%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=2x%5E2%2B+23=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B+23=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2=-+23 ALIGN=MIDDLE  ALT=\"2x%5E2=-+23\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-+23%2F2 ALIGN=MIDDLE  ALT=\"x%5E2=-+23%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28-+23%2F2%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28-+23%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=++i%2Asqrt%28+23%2F2%29%29 ALIGN=MIDDLE  ALT=\"x=++i%2Asqrt%28+23%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "two complex solutions are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=i%2Asqrt%2823%2F2%29 ALIGN=MIDDLE  ALT=\"x=i%2Asqrt%2823%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=-i%2Asqrt%2823%2F2%29+ ALIGN=MIDDLE  ALT=\"+x=-i%2Asqrt%2823%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+9%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+9%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=9 ALIGN=MIDDLE  ALT=\"x%5E2+=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%289%29 ALIGN=MIDDLE  ALT=\"x=sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><BR>\n" );
document.write( "two real solutions: <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;\" > and <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( " </SPAN>\n" );
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