document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=932792>Question 932792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the equation x^2 - 12x + y^2 - 16y + 84=0, complete the square for both x and y. What is the result? How do I do this?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #566403 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=566403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+12x+%2B+y%5E2+-+16y+%2B+84=0 ALIGN=MIDDLE  ALT=\"x%5E2+-+12x+%2B+y%5E2+-+16y+%2B+84=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%5E2+-+12x%2B__%29+%2B+%28y%5E2+-+16y+%2B__%29%2B+84=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x%2B__%29+%2B+%28y%5E2+-+16y+%2B__%29%2B+84=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since we need <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and we are given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+12x%2B_b%5E2_%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x%2B_b%5E2_%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=12 ALIGN=MIDDLE  ALT=\"2ab=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,then =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=12 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=36 ALIGN=MIDDLE  ALT=\"b%5E2=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2+-+16y+%2B_b%5E2_%29 ALIGN=MIDDLE  ALT=\"%28y%5E2+-+16y+%2B_b%5E2_%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=-16 ALIGN=MIDDLE  ALT=\"2ab=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >,then =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=-16 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=64 ALIGN=MIDDLE  ALT=\"b%5E2=64\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, to complete the square, first write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2B64-16 ALIGN=MIDDLE  ALT=\"36%2B64-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >}, add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+12x%2B_b%5E2_%29+-b%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x%2B_b%5E2_%29+-b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and subtract it so the equation doesn't change\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+12x%2B36%29+-36%2B+%28y%5E2+-+16y+%2B64%29-64%2B+84=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x%2B36%29+-36%2B+%28y%5E2+-+16y+%2B64%29-64%2B+84=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%5E2+-+6%29%5E2+%2B+%28y%5E2+-8%29%5E2-36-64%2B+84=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+6%29%5E2+%2B+%28y%5E2+-8%29%5E2-36-64%2B+84=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%5E2+-+6%29%5E2+%2B+%28y%5E2+-8%29%5E2-100%2B+84=0 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+6%29%5E2+%2B+%28y%5E2+-8%29%5E2-100%2B+84=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%5E2-6%29%5E2%2B%28y%5E2-8%29%5E2-16+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2-6%29%5E2%2B%28y%5E2-8%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%5E2-6%29%5E2%2B%28y%5E2-8%29%5E2=16+ ALIGN=MIDDLE  ALT=\"%28x%5E2-6%29%5E2%2B%28y%5E2-8%29%5E2=16+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, you have a circle with center at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   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=drawing%28+600%2C+600%2C+-5%2C+10%2C+-5%2C+15%2Clocate%286%2C8%2CC%286%2C8%29%29%2Ccircle%286%2C8%2C.12%29%2C+circle%286%2C8%2C4%29%2C+graph%28+600%2C+600%2C+-5%2C+10%2C+-5%2C+15%2C0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " </SPAN>\n" );
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