document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202846>Question 202846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve. e^(4x^2+12x+9)= 1<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153009 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=153009\">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=e%5E%284x%5E2%2B12x%2B9%29=1 ALIGN=MIDDLE  ALT=\"e%5E%284x%5E2%2B12x%2B9%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28e%5E%284x%5E2%2B12x%2B9%29%29=ln%281%29 ALIGN=MIDDLE  ALT=\"ln%28e%5E%284x%5E2%2B12x%2B9%29%29=ln%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the natural log of both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2B9=ln%281%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B9=ln%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%284x%5E2%2B12x%2B9%29 ALIGN=MIDDLE  ALT=\"e%5E%284x%5E2%2B12x%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2B9 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B9\"   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=4x%5E2%2B12x%2B9=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate the natural log of 1 to get 0\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B12x%2B9 ALIGN=MIDDLE  ALT=\"4x%5E2%2B12x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E2%2BBx%2BC ALIGN=MIDDLE  ALT=\"Ax%5E2%2BBx%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=12 ALIGN=MIDDLE  ALT=\"B=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=9 ALIGN=MIDDLE  ALT=\"C=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"x\":\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%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4 ALIGN=MIDDLE  ALT=\"A=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=12 ALIGN=MIDDLE  ALT=\"B=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=9 ALIGN=MIDDLE  ALT=\"C=9\"   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+=+%28-12+%2B-+sqrt%28+144-4%284%29%289%29+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+144-4%284%29%289%29+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   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+=+%28-12+%2B-+sqrt%28+144-144+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+144-144+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%284%29%289%29 ALIGN=MIDDLE  ALT=\"4%284%29%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   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+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%282%284%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%282%284%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   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+=+%28-12+%2B-+0%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B-+0%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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+=+%28-12+%2B+0%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+%2B+0%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12+-+0%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12+-+0%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-12%29%2F%288%29 ALIGN=MIDDLE  ALT=\"x+=++%28-12%29%2F%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F2 ALIGN=MIDDLE  ALT=\"x+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F2 ALIGN=MIDDLE  ALT=\"x+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F2 ALIGN=MIDDLE  ALT=\"x+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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