document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=428435>Question 428435</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's are the steps to deriving a quadratic formula, and can you explain how you did each step? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #297796 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=297796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the general form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28b%2Fa%29x+%2B+%28c%2Fa%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. To complete the square, we want the constant term to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2F2a%29%5E2 ALIGN=MIDDLE  ALT=\"%28b%2F2a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2F4a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2F4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2F4a%5E2+-+c%2Fa ALIGN=MIDDLE  ALT=\"b%5E2%2F4a%5E2+-+c%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28b%2Fa%29x+%2B+b%5E2%2F4a%5E2+=+b%5E2%2F4a%5E2+-+c%2Fa+=+%28b%5E2+-+4ac%29%2F4a%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >. The left side factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+b%2F2a%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+b%2F2a%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so the equation is equivalent to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+b%2F2a%29%5E2+=+%28b%5E2+-+4ac%29%2F4a%5E2 ALIGN=MIDDLE  ALT=\"%28x+%2B+b%2F2a%29%5E2+=+%28b%5E2+-+4ac%29%2F4a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Taking square root of both sides,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+b%2F2a+=+%280+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+%2B+b%2F2a+=+%280+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > <-- and there's the quadratic formula. </SPAN>\n" );
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