document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=518603>Question 518603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Complete the square to solve the following  quadratic equation for y. Show your work. \r<BR>\n" );
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document.write( "ay^2 + by +c = 0 \r<BR>\n" );
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document.write( "Why is this an important problem?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #345227 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=345227\">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( "Ah ha!  Now that is different.  This is an important problem because it gives you the general solution to the quadratic equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ay^2\ +\ by\ +\ c\ =\ 0\">\r<BR>\n" );
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document.write( "Add the opposite of the constant term to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ay^2\ +\ by\ =\ -c\">\r<BR>\n" );
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document.write( "Multiply both sides by the reciprocal of the lead coefficient:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y^2\ +\ \frac{b}{a}y\ =\ -\frac{c}{a}\">\r<BR>\n" );
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document.write( "Divide the first degree term coefficient by 2, square the result, and then add it to both sides:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y^2\ +\ \frac{b}{a}y +\ \frac{b^2}{4a^2}\ =\ \frac{b^2}{4a^2}\ -\ \frac{c}{a}\">\r<BR>\n" );
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document.write( "Apply the common denominator in the RHS:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y^2\ +\ \frac{b}{a}y +\ \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(y\ +\ \frac{b}{2a}\right)^2\ =\ \frac{b^2\ -\ 4ac}{4a^2}\">\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 \ \ \ \ \ \ \ \ \ \ y\ +\ \frac{b}{2a}\ =\ \pm\ \frac{\sqrt{b^2\ -\ 4ac}}{2a}\">\r<BR>\n" );
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document.write( "Add the opposite of the LHS constant term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\  \frac{-b\ \pm\ \sqrt{b^2\ -\ 4ac}}{2a}\">\r<BR>\n" );
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document.write( "Now you can solve all quadratic equations of the form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ ay^2\ +\ by\ +\ c\ =\ 0\">\r<BR>\n" );
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document.write( "just by doing some arithmetic with the coefficients.\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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