document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=766193>Question 766193</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x+16/x=8\r<BR>\n" );
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document.write( "Find the roots (values of x when the expression is equal to zero) using factoring.  Prove your answers are correct by checking, or showing that the values of x you computed satisfy the original equation.\r<BR>\n" );
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document.write( "- 8 from both sides x-8+16/x=0 to get rid of fraction <BR>\n" );
document.write( "x^2-8x+16=0\r<BR>\n" );
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document.write( "x=4 <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 #466717 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=466717\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You are half right.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ -\ 8x\ +\ 16\ =\ 0\">\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/rendertex.cgi?\LARGE (x\ -\ 4)(x\ -\ 4)\ =\ 0\">\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ 4\"> or <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ 4\">\r<BR>\n" );
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document.write( "ALL quadratics have two roots.  That is because all <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE n\">-th degree polynomial equations have <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE n\"> roots,  c.f. The Fundamental Theorem of Algebra.\r<BR>\n" );
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document.write( "By the way, you have a mis-statement in your solution, though the outcome was correct.  Adding -8 to both sides doesn't do anything about the variable in the denominator.  You have to multiply, in this case by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\">, to get rid of the fraction.\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" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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