document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188987>Question 188987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> radical b^2+16+2b = 5b\r<BR>\n" );
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document.write( "b^2 + 16 + 2b = 25b^2\r<BR>\n" );
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document.write( "0 = 24b^2 - 2b - 16\r<BR>\n" );
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document.write( "0= 2(12b^2 - b - 8)\r<BR>\n" );
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document.write( "then what?\r<BR>\n" );
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document.write( "I know the answer is the square root of 2, but don't know how to get there from here. <BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141740 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=141740\">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( "So, you know the answer is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large sqrt{2}\">.  Well, let's just find out if that is correct.\r<BR>\n" );
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document.write( "If\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  sqrt{b^2 + 16 + 2b} = 5b\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  b = sqrt{2}\">\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  sqrt{( \sqrt{2} )^2 + 16 + 2( \sqrt{2})} = 5 sqrt{2}\">\r<BR>\n" );
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document.write( "Well, root 2 squared is just 2 plus 16 is 18 plus 2 times root 2 which is a little less than 3, so total somewhere between 20 and 21, take the root of that and you get maybe 4 and a half.  But 5 times root 2 is a little less than 7 and a half.  < <i><b>Buzz</b></i> > Thank you for playing, we have some lovely parting gifts.\r<BR>\n" );
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document.write( "Once you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 0= 2(12b^2 - b - 8)\">\r<BR>\n" );
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document.write( "You know that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 12b^2 - b - 8 = 0\">\r<BR>\n" );
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document.write( "Just use the quadratic formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b_{1,2} = \frac{-\beta \pm sqrt{\beta^2 - 4\alpha\gamma}}{2\alpha}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \alpha = 12\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \beta = -1\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \gamma = -8\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ b_{1,2} = \frac{-1 \pm sqrt{(-1)^2 - 4(12)(-8)}}{2(12)}\">\r<BR>\n" );
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document.write( "You get to do your own arithmetic.\r<BR>\n" );
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document.write( "You will get two roots to the quadratic, but in the process of squaring the variable you quite often get an extraneous root.  One of the roots to this equation will be extraneous, so you have to check both answers in the original equation to determine which one to throw out.\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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