document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=691174>Question 691174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble solving this equation for x. Could you help me? Thanks! \r<BR>\n" );
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document.write( "2e^x + 4xe^x + (x^2-1)e^x = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426547 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=426547\">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=2e%5Ex+%2B+4xe%5Ex+%2B+%28x%5E2-1%29e%5Ex+=+0 ALIGN=MIDDLE  ALT=\"2e%5Ex+%2B+4xe%5Ex+%2B+%28x%5E2-1%29e%5Ex+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....first multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-1%29e%5Ex ALIGN=MIDDLE  ALT=\"%28x%5E2-1%29e%5Ex\"   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=2e%5Ex+%2B+4xe%5Ex+%2B+x%5E2e%5Ex-1e%5Ex=+0 ALIGN=MIDDLE  ALT=\"2e%5Ex+%2B+4xe%5Ex+%2B+x%5E2e%5Ex-1e%5Ex=+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%5E2e%5Ex+%2B+4xe%5Ex+%2Be%5Ex=+0 ALIGN=MIDDLE  ALT=\"x%5E2e%5Ex+%2B+4xe%5Ex+%2Be%5Ex=+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=e%5Ex%2Ax%5E2+%2B+4e%5Ex%2Ax+%2Be%5Ex=+0 ALIGN=MIDDLE  ALT=\"e%5Ex%2Ax%5E2+%2B+4e%5Ex%2Ax+%2Be%5Ex=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....here you have a quadratic equation (in general form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=e%5Ex ALIGN=MIDDLE  ALT=\"a=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4e%5Ex ALIGN=MIDDLE  ALT=\"b=4e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=e%5Ex ALIGN=MIDDLE  ALT=\"c=e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now you use quadratic formula to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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-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;\" > ....plug in values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   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+=+%28-4e%5Ex+%2B-+sqrt%28%284e%5Ex%29%5E2-4%2Ae%5Ex%2Ae%5Ex+%29%29%2F%282%2Ae%5Ex%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4e%5Ex+%2B-+sqrt%28%284e%5Ex%29%5E2-4%2Ae%5Ex%2Ae%5Ex+%29%29%2F%282%2Ae%5Ex%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+=+%28-4e%5Ex+%2B-+sqrt%2816e%5E%282x%29-4%2Ae%5E%282x%29+%29%29%2F%282e%5Ex%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4e%5Ex+%2B-+sqrt%2816e%5E%282x%29-4%2Ae%5E%282x%29+%29%29%2F%282e%5Ex%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+=+%28-4e%5Ex+%2B-+sqrt%2812e%5E%282x%29+%29%29%2F%282e%5Ex%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4e%5Ex+%2B-+sqrt%2812e%5E%282x%29+%29%29%2F%282e%5Ex%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%282x%29=%28e%5Ex%29%5E2 ALIGN=MIDDLE  ALT=\"e%5E%282x%29=%28e%5Ex%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4e%5Ex+%2B-+sqrt%284%2A3%28e%5Ex%29%5E2+%29%29%2F%282e%5Ex%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4e%5Ex+%2B-+sqrt%284%2A3%28e%5Ex%29%5E2+%29%29%2F%282e%5Ex%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+=+%28-4e%5Ex+%2B-+2%28e%5Ex%29sqrt%283+%29%29%2F%282e%5Ex%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-4e%5Ex+%2B-+2%28e%5Ex%29sqrt%283+%29%29%2F%282e%5Ex%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F2%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+=+%281%2F2%29%28%28-4cross%28%28e%5Ex%29%29+%2B-+2cross%28%28e%5Ex%29%29sqrt%283+%29%29%2Fcross%28%28e%5Ex%29%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.....cancel <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28e%5Ex%29 ALIGN=MIDDLE  ALT=\"%28e%5Ex%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+=+%281%2F2%29%28-4+%2B-+2sqrt%283+%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4+%2B-+2sqrt%283+%29%29+\"   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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F2%29%28-4+%2B+2sqrt%283+%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4+%2B+2sqrt%283+%29%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+=+%281%2F2%29%28-4+%2B+2%2A1.73%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4+%2B+2%2A1.73%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+=+%281%2F2%29%28-4+%2B+3.46%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4+%2B+3.46%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+=+%281%2F2%29%28-0.54%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-0.54%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+=-0.27 ALIGN=MIDDLE  ALT=\"x+=-0.27\"   DISABLED_style= \"max-width:90%; height:auto;\" >............if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-0.27 ALIGN=MIDDLE  ALT=\"x+=-0.27\"   DISABLED_style= \"max-width:90%; height:auto;\" > in given equation, you will get answer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.00541999 ALIGN=MIDDLE  ALT=\"-0.00541999\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is rounded to whole number equal to zero\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2F2%29%28-4+-2sqrt%283+%29%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4+-2sqrt%283+%29%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+=+%281%2F2%29%28-4-2%2A1.73%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4-2%2A1.73%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+=+%281%2F2%29%28-4+-+3.46%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-4+-+3.46%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+=+%281%2F2%29%28-7.46%29+ ALIGN=MIDDLE  ALT=\"x+=+%281%2F2%29%28-7.46%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+=-3.73 ALIGN=MIDDLE  ALT=\"x+=-3.73\"   DISABLED_style= \"max-width:90%; height:auto;\" >...........if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-3.73 ALIGN=MIDDLE  ALT=\"x+=-3.73\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.000170349 ALIGN=MIDDLE  ALT=\"-0.000170349\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you also round it to zero\r<BR>\n" );
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document.write( "the difference appears because rounding decimals during calculation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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