document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045637>Question 1045637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the standard form of the equation x^2+3y^2+4x+6y+1=0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661154 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=661154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the standard form of the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3y%5E2%2B4x%2B6y%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3y%5E2%2B4x%2B6y%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3y%5E2%2B4x%2B6y%2B1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3y%5E2%2B4x%2B6y%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%29%2B%283y%5E2%2B6y%29%2B1=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%29%2B%283y%5E2%2B6y%29%2B1=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%2B4x%29%2B3%28y%5E2%2B2y%29%2B1=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%29%2B3%28y%5E2%2B2y%29%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......complete squares\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2Bb%5E2%29-b%5E2%2B3%28y%5E2%2B2y%2Bb%5E2%29-3b%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2Bb%5E2%29-b%5E2%2B3%28y%5E2%2B2y%2Bb%5E2%29-3b%5E2%2B1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....recall, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and in your case for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=4 ALIGN=MIDDLE  ALT=\"2ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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=2%2A1%2Ab=4 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F2 ALIGN=MIDDLE  ALT=\"b=4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%5E2%2B2y%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"3%28y%5E2%2B2y%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=2 ALIGN=MIDDLE  ALT=\"2ab=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we can find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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=2%2A1%2Ab=2 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=2 ALIGN=MIDDLE  ALT=\"2b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2B2%5E2%29-2%5E2%2B3%28y%5E2%2B2y%2B1%5E2%29-3%2A1%5E2%2B1=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2B2%5E2%29-2%5E2%2B3%28y%5E2%2B2y%2B1%5E2%29-3%2A1%5E2%2B1=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%2B2%29%5E2-4%2B3%28y%2B1%29%5E2-3%2B1=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2-4%2B3%28y%2B1%29%5E2-3%2B1=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%2B2%29%5E2%2B3%28y%2B1%29%5E2-7%2B1=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B3%28y%2B1%29%5E2-7%2B1=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%2B2%29%5E2%2B3%28y%2B1%29%5E2-6=0 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B3%28y%2B1%29%5E2-6=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%2B2%29%5E2%2B3%28y%2B1%29%5E2=6 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2B3%28y%2B1%29%5E2=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >..............both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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%2B2%29%5E2%2F6%2B3%28y%2B1%29%5E2%2F6=6%2F6 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2F6%2B3%28y%2B1%29%5E2%2F6=6%2F6\"   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%2B2%29%5E2%2F6%2Bcross%283%29%28y%2B1%29%5E2%2Fcross%286%292=1 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2F6%2Bcross%283%29%28y%2B1%29%5E2%2Fcross%286%292=1\"   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%2B2%29%5E2%2F6%2B%28y%2B1%29%5E2%2F2=1 ALIGN=MIDDLE  ALT=\"%28x%2B2%29%5E2%2F6%2B%28y%2B1%29%5E2%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> you have an ellipse and this is the standard form of the equation\r<BR>\n" );
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document.write( " </SPAN>\n" );
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