document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7474>Question 7474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to solve this quadratic equation by completing the square<BR>\n" );
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document.write( "x^2   + 6X - 7 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4128 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ok, completing the square...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-7 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >. First ignore the 7. Just think about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x ALIGN=MIDDLE  ALT=\"x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >. What i want to do is think of the correct number (not the 7) that needs to be there so that I can factorise the quadratic as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bk%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bk%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k is a \"nice\" number, usually an integer, sometimes a simple fraction, rarely a horrible number.\r<BR>\n" );
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document.write( "think about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bk%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bk%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This expands to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2kx+%2B+k%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2kx+%2B+k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we look at the coefficient before the x-term, our +6, and we note that this is like the \"2k\", so k must be 3. The number we therefore require <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2%29 ALIGN=MIDDLE  ALT=\"%28k%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is +9, so what we need is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B9 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "That is it done, really. All we have to do now is get this to look like the original, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-7 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B9-9-7 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B9-9-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >...note the +9-9 cancel each other out, leaving the -7<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x%2B9+-+16 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x%2B9+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2+-+16 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2+-+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Hope this is clear?\r<BR>\n" );
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document.write( "And now to answer the question... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2+-+16+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2+-+16+=+0\"   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=%28x%2B3%29%5E2+=+16 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29+=+sqrt%2816%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29+=+sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29+=+-+sqrt%2816%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29+=+-+sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so x+3 = 4 OR x+3 = -4<BR>\n" );
document.write( "so x=1 OR x=-7\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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