document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=258000>Question 258000</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the points of intersection of these equations <BR>\n" );
document.write( "x-2y-8=0<BR>\n" );
document.write( "x^2=y^2-12x+6y+29=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189894 by </B><A HREF=/tutors/aboutme.mpl?userid=Greenfinch><B>Greenfinch(383)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Greenfinch><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=Greenfinch><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189894\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Second equation is a circle, so reorganise it<BR>\n" );
document.write( "(x^2 + 12 x) - (y^2 - 6y)+ 29 = 0 and then complete the square<BR>\n" );
document.write( "(x^2 + 12x + 36) - ( y^2 - 6y + 9) - 45 + 29 = 0 which becomes<BR>\n" );
document.write( "(x + 6)^2 - (y - 3)^2 = 4^2 which is a circle centre at -6, 3 and radius 4<BR>\n" );
document.write( "other equation is y = (1/2)x - 4 or x = 2y + 8<BR>\n" );
document.write( "Probably solve for y is easier<BR>\n" );
document.write( "(2y + 14)^2 - (y - 3)^2 = 4^2<BR>\n" );
document.write( "4y^2 + 56 y + 196 -(y^2 - 6y +9) = 16<BR>\n" );
document.write( "3y^2 + 62y + 187 = 16<BR>\n" );
document.write( "3y^2 + 62y + 171 = 0<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ay%5E2%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ay%5E2%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2%2B62y%2B171+=+0 ALIGN=MIDDLE  ALT=\"3y%5E2%2B62y%2B171+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2862%29%5E2-4%2A3%2A171=1792 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2862%29%5E2-4%2A3%2A171=1792\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1792 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-62%2B-sqrt%28+1792+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-62%2B-sqrt%28+1792+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+%28-%2862%29%2Bsqrt%28+1792+%29%29%2F2%5C3+=+-3.27799650382776 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+%28-%2862%29%2Bsqrt%28+1792+%29%29%2F2%5C3+=+-3.27799650382776\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+%28-%2862%29-sqrt%28+1792+%29%29%2F2%5C3+=+-17.3886701628389 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+%28-%2862%29-sqrt%28+1792+%29%29%2F2%5C3+=+-17.3886701628389\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2%2B62y%2B171 ALIGN=MIDDLE  ALT=\"3y%5E2%2B62y%2B171\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3y%5E2%2B62y%2B171+=+3%28y--3.27799650382776%29%2A%28y--17.3886701628389%29 ALIGN=MIDDLE  ALT=\"3y%5E2%2B62y%2B171+=+3%28y--3.27799650382776%29%2A%28y--17.3886701628389%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -3.27799650382776, -17.3886701628389.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B62%2Ax%2B171+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B62%2Ax%2B171+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Then use x = 2y + 8 to get the x figures </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );