document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=326091>Question 326091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 18d^2+36d+10=0\r<BR>\n" );
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document.write( "The answer is - 1/5 , - 1/3  I just don't know how to get there </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233402 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18x^2\ +\ 36x +\ 10\ =\ 0\">\r<BR>\n" );
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document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-1}{3}\"> is a root, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18\left(\frac{-1}{3}\right)^2\ +\ 36\left(\frac{-1}{3}\right) +\ 10\ =\ 0\ \Rightarrow\ 2\ -\ 12\ +\ 10\ =\ 0\">\r<BR>\n" );
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document.write( "Which is true.  So far, so good, plus a good side-effect is that we know that one of the factors of the trinomial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 1\">\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-1}{5}\"> is a root, then:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18\left(\frac{-1}{5}\right)^2\ +\ 36\left(\frac{-1}{5}\right) +\ 10\ =\ 0\ \Rightarrow\ \frac{18}{25}\ -\ \frac{36}{5}\ +\ 10\ =\ 3.52 \neq\ 0\">\r<BR>\n" );
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document.write( "Oops! Warning! Danger, Will Robinson.  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{-1}{5}\"> is NOT a root of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18x^2\ +\ 36x +\ 10\ =\ 0\">\r<BR>\n" );
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document.write( "Let's go back and factor.  First take out a 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9x^2\ +\ 18x +\ 5\ =\ 0\">\r<BR>\n" );
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document.write( "Since we know that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 1\"> is a factor, the other factor has to be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 5\">.  Verify using FOIL (left as an exercise for the student.)\r<BR>\n" );
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document.write( "Since the other factor is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 3x\ +\ 5\">, the second root must be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -\frac{5}{3}\">\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 18\left(\frac{-5}{3}\right)^2\ +\ 36\left(\frac{-5}{3}\right) +\ 10\ =\ 0\ \Rightarrow\ 50\ -\ 60\ +\ 10\ =\ 0\">\r<BR>\n" );
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document.write( "Answer checks.  Who told you the answers?  Go get your money back.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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