document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436202>Question 436202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (x-2)^2/9+(y-3)^2/36=1<BR>\n" );
document.write( "y= -1/2x+4\r<BR>\n" );
document.write( "\n" );
document.write( "the first equation needs to be written so that it has a y= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301793 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=301793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x-2)^2/9+(y-3)^2/36=1<BR>\n" );
document.write( "y= -1/2x+4\r<BR>\n" );
document.write( "\n" );
document.write( "the first equation needs to be written so that it has a y=<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Sub for y in the 1st eqn and multiply thru by 36<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%28x-2%29%5E2+%2B+%28-x%2F2+%2B+1%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"4%2A%28x-2%29%5E2+%2B+%28-x%2F2+%2B+1%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+-+16x+%2B+16+%2B+x%5E2%2F4+-+x+%2B+1+=+36 ALIGN=MIDDLE  ALT=\"4x%5E2+-+16x+%2B+16+%2B+x%5E2%2F4+-+x+%2B+1+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16x%5E2+-+64x+%2B+64+%2B+x%5E2+-+4x+%2B+4+=+144 ALIGN=MIDDLE  ALT=\"16x%5E2+-+64x+%2B+64+%2B+x%5E2+-+4x+%2B+4+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%5E2+-+68x+%2B+68+=+144 ALIGN=MIDDLE  ALT=\"17x%5E2+-+68x+%2B+68+=+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17x%5E2+-+68x+-+76+=+0 ALIGN=MIDDLE  ALT=\"17x%5E2+-+68x+-+76+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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=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=17x%5E2%2B-68x%2B-76+=+0 ALIGN=MIDDLE  ALT=\"17x%5E2%2B-68x%2B-76+=+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=%28-68%29%5E2-4%2A17%2A-76=9792 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-68%29%5E2-4%2A17%2A-76=9792\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=9792 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--68%2B-sqrt%28+9792+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--68%2B-sqrt%28+9792+%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-%28-68%29%2Bsqrt%28+9792+%29%29%2F2%5C17+=+4.910427500436 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-68%29%2Bsqrt%28+9792+%29%29%2F2%5C17+=+4.910427500436\"   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-%28-68%29-sqrt%28+9792+%29%29%2F2%5C17+=+-0.910427500435996 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-68%29-sqrt%28+9792+%29%29%2F2%5C17+=+-0.910427500435996\"   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=17x%5E2%2B-68x%2B-76 ALIGN=MIDDLE  ALT=\"17x%5E2%2B-68x%2B-76\"   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=17x%5E2%2B-68x%2B-76+=+%28x-4.910427500436%29%2A%28x--0.910427500435996%29 ALIGN=MIDDLE  ALT=\"17x%5E2%2B-68x%2B-76+=+%28x-4.910427500436%29%2A%28x--0.910427500435996%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4.910427500436, -0.910427500435996.\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+17%2Ax%5E2%2B-68%2Ax%2B-76+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+17%2Ax%5E2%2B-68%2Ax%2B-76+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "--------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2+-+12sqrt%2817%29%2F17 ALIGN=MIDDLE  ALT=\"x+=+2+-+12sqrt%2817%29%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3+%2B+6sqrt%2817%29%2F17 ALIGN=MIDDLE  ALT=\"y+=+3+%2B+6sqrt%2817%29%2F17\"   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+=+2+%2B+12sqrt%2817%29%2F17 ALIGN=MIDDLE  ALT=\"x+=+2+%2B+12sqrt%2817%29%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3+-+6sqrt%2817%29%2F17 ALIGN=MIDDLE  ALT=\"y+=+3+-+6sqrt%2817%29%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );