document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093133>Question 1093133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. 3x -2y =0<BR>\n" );
document.write( "   x^2+(y-1)^2=11\r<BR>\n" );
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document.write( "2. 6x +12y^2-18=0<BR>\n" );
document.write( "   y+3x-9=0\r<BR>\n" );
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document.write( "3.12x^2-y^2-12=0<BR>\n" );
document.write( "  y-2 =0\r<BR>\n" );
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document.write( "4. 8x^2-y^2+16y-18=0<BR>\n" );
document.write( "   2y^2-48x -16y - 3 = 0\r<BR>\n" );
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document.write( "Good day Sir/Mam! <BR>\n" );
document.write( "What is the solution set of this  non linear equation and the steps? <BR>\n" );
document.write( "Thank You I truly appreciate your website. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707769 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. 3x -2y =0<BR>\n" );
document.write( "   x^2+(y-1)^2=11<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "3x -2y =0<BR>\n" );
document.write( "3x = 2y<BR>\n" );
document.write( "9x^2 = 4y^2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "x^2+(y-1)^2=11<BR>\n" );
document.write( "9x^2 + 9(y-1)^2 = 99<BR>\n" );
document.write( "Sub for 9x^2<BR>\n" );
document.write( "4y^2 + 9y^2 - 18y + 9 = 99<BR>\n" );
document.write( "13y^2 - 18y - 90 = 0<BR>\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13x%5E2%2B-18x%2B-90+=+0 ALIGN=MIDDLE  ALT=\"13x%5E2%2B-18x%2B-90+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-18%29%5E2-4%2A13%2A-90=5004 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-18%29%5E2-4%2A13%2A-90=5004\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5004 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--18%2B-sqrt%28+5004+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--18%2B-sqrt%28+5004+%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=x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+5004+%29%29%2F2%5C13+=+3.41303679751191 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+5004+%29%29%2F2%5C13+=+3.41303679751191\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-18%29-sqrt%28+5004+%29%29%2F2%5C13+=+-2.02842141289652 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-18%29-sqrt%28+5004+%29%29%2F2%5C13+=+-2.02842141289652\"   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=13x%5E2%2B-18x%2B-90 ALIGN=MIDDLE  ALT=\"13x%5E2%2B-18x%2B-90\"   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=13x%5E2%2B-18x%2B-90+=+%28x-3.41303679751191%29%2A%28x--2.02842141289652%29 ALIGN=MIDDLE  ALT=\"13x%5E2%2B-18x%2B-90+=+%28x-3.41303679751191%29%2A%28x--2.02842141289652%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.41303679751191, -2.02842141289652.\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+13%2Ax%5E2%2B-18%2Ax%2B-90+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+13%2Ax%5E2%2B-18%2Ax%2B-90+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "y = the unfortunate answers shown.<BR>\n" );
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document.write( "x = 2y/3<BR>\n" );
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document.write( "2. 6x +12y^2-18=0 --> 3x + 6y^2 - 9 = 0<BR>\n" );
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document.write( "   y+3x-9=0<BR>\n" );
document.write( "3x = -y+9<BR>\n" );
document.write( "Sub for 3x in the 1st eqn.<BR>\n" );
document.write( "===============\r<BR>\n" );
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document.write( "3.12x^2-y^2-12=0<BR>\n" );
document.write( "  y-2 =0<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "Sub for y<BR>\n" );
document.write( "====================\r<BR>\n" );
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document.write( "4. 8x^2-y^2+16y-18=0<BR>\n" );
document.write( "   2y^2-48x -16y - 3 = 0<BR>\n" );
document.write( "Solve eqn 2 for x, then sub for x in eqn 1.<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Check for extraneous solutions.\r<BR>\n" );
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