document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=674484>Question 674484</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need help solving this equation without using the quadratic formula: x^2-1/2x=1/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #419296 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=419296\">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( "The only way to do it, since it won't factor and you don't want to use the quadratic formula, is to complete the square.\r<BR>\n" );
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document.write( "Divide the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> by 2, then square the result:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(\frac{1}{4}\right)^2\ =\ \frac{1}{16}\">.  Add to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2\ -\ \frac{1}{2}\ +\ \frac{1}{16}\ =\ \frac{1}{3}\ +\ \frac{1}{16}\">\r<BR>\n" );
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document.write( "Factor the perfect square trinomial in the LHS and simplify the RHS.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(x\ -\ \frac{1}{4}\right)^2\ =\ \frac{19}{48}\">\r<BR>\n" );
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document.write( "Take the square root of both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ -\ \frac{1}{4}\ =\ \pm\ \sqrt{\frac{19}{48}}\">\r<BR>\n" );
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document.write( "Add the additive inverse of the constant in the LHS to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ =\ \frac{1}{4}\ \pm\ \sqrt{\frac{19}{48}}\">\r<BR>\n" );
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document.write( "Now all you have to do is to rationalize the denominator and apply the LCD to combine the two fractions in the RHS.\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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