document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391285>Question 391285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the quadratic formula?<BR>\n" );
document.write( "what is the origin of the quadratic formula? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277579 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=277579\">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( "The quadratic formula gives the general solution of a quadratic equation.  The formula was developed by completeing the square on the general quadratic equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ +\ c\ =\ 0\">\r<BR>\n" );
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document.write( "Move the constant term to the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ax^2\ +\ bx\ =\ -\ c\">\r<BR>\n" );
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document.write( "Divide by the lead coefficient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \frac{b}{a}x\ =\ -\ \frac{c}{a}\">\r<BR>\n" );
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document.write( "Divide the coefficient on the 1st degree term by 2, square the result, then add that result to both sides 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\ +\ \frac{b}{a}x\ +\ \frac{b^2}{4a^2}\ =\  \frac{b^2}{4a^2}\ -\ \frac{c}{a}\">\r<BR>\n" );
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document.write( "Apply the LCD and complete the sum in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ \frac{b}{a}x\ +\ \frac{b^2}{4a^2}\ =\  \frac{b^2\ -\ 4ac}{4a^2}\">\r<BR>\n" );
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document.write( "Factor the perfect square in the LHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(x\ +\ \frac{b}{2a}\right)^2\ =\  \frac{b^2\ -\ 4ac}{4a^2}\">\r<BR>\n" );
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document.write( "Take the square root remembering to consider both the positive and negative root:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x\ +\ \frac{b}{2a}\ =\  \pm\sqrt{\frac{b^2\ -\ 4ac}{4a^2}}\ =\ \frac{\pm\sqrt{b^2\ -\ 4ac}}{2a}\">\r<BR>\n" );
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document.write( "Add <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{b}{2a}\"> 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{-b\ \pm\sqrt{b^2\ -\ 4ac}}{2a}\">\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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