document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200474>Question 200474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have two equations that I cant seem to solve because I dont understand.  I have been trying to solve for two days, yes I am very rusty with this it has ben over 10yrs since I had to do algebra.  If you could please help it wold be greatly appreciated.  Tahnk you. Nakia\r<BR>\n" );
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document.write( "x^2+y^2+10x+14y+73=0\r<BR>\n" );
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document.write( "36x^2+36y^2+48x-36y-11=0\r<BR>\n" );
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document.write( "the directions for this equation tells me to find the center and length of a radius of each circle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150781 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B10x%2B14y%2B73=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B10x%2B14y%2B73=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B10x%2B14y=-73 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B10x%2B14y=-73\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=73 ALIGN=MIDDLE  ALT=\"73\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B10x%29%2B%28y%5E2%2B14y%29=-73 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B10x%29%2B%28y%5E2%2B14y%29=-73\"   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%2B5%29%5E2-25%2B%28y%5E2%2B14y%29=-73 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2-25%2B%28y%5E2%2B14y%29=-73\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the x terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2-25%2B%28y%2B7%29%5E2-49=-73 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2-25%2B%28y%2B7%29%5E2-49=-73\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the y terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2%2B%28y%2B7%29%5E2-74=-73 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2%2B%28y%2B7%29%5E2-74=-73\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2%2B%28y%2B7%29%5E2=-73%2B74 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2%2B%28y%2B7%29%5E2=-73%2B74\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=74 ALIGN=MIDDLE  ALT=\"74\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%5E2%2B%28y%2B7%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%5E2%2B%28y%2B7%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-5%29%29%5E2%2B%28y%2B7%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-%28-5%29%29%5E2%2B%28y%2B7%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5 ALIGN=MIDDLE  ALT=\"x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%28-5%29 ALIGN=MIDDLE  ALT=\"x-%28-5%29\"   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-%28-5%29%29%5E2%2B%28y-%28-7%29%29%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-%28-5%29%29%5E2%2B%28y-%28-7%29%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B7 ALIGN=MIDDLE  ALT=\"y%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-7%29 ALIGN=MIDDLE  ALT=\"y-%28-7%29\"   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-%28-5%29%29%5E2%2B%28y-%28-7%29%29%5E2=1%5E2 ALIGN=MIDDLE  ALT=\"%28x-%28-5%29%29%5E2%2B%28y-%28-7%29%29%5E2=1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 1 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2 ALIGN=MIDDLE  ALT=\"1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-----------\r<BR>\n" );
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document.write( "Notice how the equation is now in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that this conic section is a circle where (h,k) is the center and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius.\r<BR>\n" );
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document.write( "In this case, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-5 ALIGN=MIDDLE  ALT=\"h=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-7 ALIGN=MIDDLE  ALT=\"k=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the circle has these properties:\r<BR>\n" );
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document.write( "CENTER: (-5,-7)\r<BR>\n" );
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document.write( "Radius: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=1 ALIGN=MIDDLE  ALT=\"r=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie the radius is one unit long)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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