document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=203863>Question 203863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> help needed:<BR>\n" );
document.write( "Give points which are outside and pont which are inside of the circles in this equation: x^2+y^2+6x=0<BR>\n" );
document.write( "p.s: could you please explain the solution for me that I can solve a group of questions like this ? Thank you:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153820 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=153820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First get your equation into the standard form for a circle whose center is at (h, k) and whose radius is r.:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the variables as shown below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B6x%29%2By%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B6x%29%2By%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now \"complete-the-square\" in the x-variable by adding the square of half the x-coefficient to both sides of the equation. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F2%29%5E2+=+9 ALIGN=MIDDLE  ALT=\"%286%2F2%29%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B6x%2B9%29%2By%5E2+=+0%2B9 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B6x%2B9%29%2By%5E2+=+0%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the trinomial in x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2By%5E2+=+9 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2By%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare this with the standard form for a circle:<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "The center of the circle is at (-3, 0) and the radius is 3.<BR>\n" );
document.write( "It's probably easier to graph the circle then pick out the appropriate points inside and outside of the circle.<BR>\n" );
document.write( "To graph the circle, you will need to solve your equation for y (you will get two solutions) then graph both solutions.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x ALIGN=MIDDLE  ALT=\"6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+-x%5E2-6x ALIGN=MIDDLE  ALT=\"y%5E2+=+-x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%28-x%5E2-6x%29 ALIGN=MIDDLE  ALT=\"y+=+sqrt%28-x%5E2-6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-sqrt%28-x%5E2-6x%29 ALIGN=MIDDLE  ALT=\"y+=+-sqrt%28-x%5E2-6x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we'll graph these two solutions on the same grid:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-8%2C8%2C-8%2C8%2Csqrt%28-x%5E2-6x%29%2C-sqrt%28-x%5E2-6x%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-8%2C8%2C-8%2C8%2Csqrt%28-x%5E2-6x%29%2C-sqrt%28-x%5E2-6x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );