document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=479772>Question 479772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please put this equation into the standard form of a conic, step-by-step?\r<BR>\n" );
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document.write( "3y^2 + 20x = 23 + 5x^2 + 12y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #328729 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=328729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Step 1: Move all variables to left side and constants to right side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283y%5E2-12y%29+%2B+%28-5x%5E2%2B20x%29=+23 ALIGN=MIDDLE  ALT=\"%283y%5E2-12y%29+%2B+%28-5x%5E2%2B20x%29=+23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use completing the square with both x and y expressions.<BR>\n" );
document.write( "Step 2: factor out leading coefficients:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%5E2-4y%29+-5%28x%5E2-4x%29+=23 ALIGN=MIDDLE  ALT=\"3%28y%5E2-4y%29+-5%28x%5E2-4x%29+=23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 3: Take 2nd coefficient, Halve it, then square it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%5E2-4y%2B4%29-5%28x%5E2-4x%2B4%29+=+23 ALIGN=MIDDLE  ALT=\"3%28y%5E2-4y%2B4%29-5%28x%5E2-4x%2B4%29+=+23\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 4: Multiply leading coefficient by number found in step 3 and add to right side.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y%5E2-4y%2B4%29-5%28x%5E2-4x%2B4%29+=+23%2B12-20+=+15 ALIGN=MIDDLE  ALT=\"3%28y%5E2-4y%2B4%29-5%28x%5E2-4x%2B4%29+=+23%2B12-20+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 5: Factor expressions, notice they are perfect squares<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28y-2%29%5E2+-5%28x-2%29%5E2+=+15 ALIGN=MIDDLE  ALT=\"3%28y-2%29%5E2+-5%28x-2%29%5E2+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Step 6: Divide equation by 15, In standard form the right side must be 1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y-2%29%5E2%29%2F5+-+%28%28x-2%29%5E2%29%2F3+=+1 ALIGN=MIDDLE  ALT=\"%28%28y-2%29%5E2%29%2F5+-+%28%28x-2%29%5E2%29%2F3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now it is in standard form: A vertical Hyperbola with center (2,2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C10%2C-8%2C12%2C2%2Bsqrt%285%2B1.666%28x-2%29%5E2%29%2C2-sqrt%285%2B1.666%28x-2%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );