document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=586507>Question 586507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the standard form of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6y%5E2-2x%2B12y-23=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6y%5E2-2x%2B12y-23=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #373779 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=373779\">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 need to complete the square on each of the variables.  Group the variables and move the constant term into the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 2x\ +\ 6y^2\ +\ 12y\ =\ 23\">\r<BR>\n" );
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document.write( "Divide the coefficient on the 1st degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> term by 2, square the result, then add that result 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\ -\ 2x\ +\ 1\ +\ 6y^2\ +\ 12y\ =\ 23\ +\ 1\">\r<BR>\n" );
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document.write( "The coefficient on the 2nd degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> term is greater than 1, so factor the coefficient from the 1st and second degree <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 2x\ +\ 1\ +\ 6(y^2\ +\ 2y\ \ \ )\ =\ 23\ +\ 1\">\r<BR>\n" );
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document.write( "Divide the coefficient on <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> by 2, square the result, and add that result INSIDE the parentheses.  Multiply what you added inside the parentheses by the factor outside the parentheses and add that result to the RHS of the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ -\ 2x\ +\ 1\ +\ 6(y^2\ +\ 2y\ +\ 1)\ =\ 23\ +\ 1\ +\ 6\">\r<BR>\n" );
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document.write( "Factor the two perfect square trinomials in the LHS and collect terms in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x\ -\ 1)^2\ +\ 6(y\ +\ 1)^2\ =\ 30\">\r<BR>\n" );
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document.write( "Divide both sides by the constant in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ -\ 1)^2}{30}\ +\ \frac{(y\ +\ 1)^2}{5}\ =\ 1\">\r<BR>\n" );
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document.write( "Re-write so that the center coordinates and the measures of the semi-axes can be determined by inspection:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ -\ 1)^2}{\left(\sqrt{30}\right)^2}\ +\ \frac{\left(y\ -\ (-1)\right)^2}{\left(\sqrt{5}\right)^2}\ =\ 1\">\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( "My calculator said it, I believe it, that settles it<BR>\n" );
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