document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=437133>Question 437133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Y+11=2X<BR>\n" );
document.write( "2X TO THE SECOND +Y TO THE SECOND = 41 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #302344 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=302344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We're told:<BR>\n" );
document.write( "y+11=2x<BR>\n" );
document.write( "Subtracting 11 from both sides:<BR>\n" );
document.write( "y = 2x -11<BR>\n" );
document.write( ".<BR>\n" );
document.write( "We're told:<BR>\n" );
document.write( "x^2 + y^2 = 41<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute y = 2x-11:<BR>\n" );
document.write( "x^2 + (2x-11)^2 = 41<BR>\n" );
document.write( "x^2 + 4x^2 -44x + 121 = 41<BR>\n" );
document.write( "5x^2 -44x +80 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This will not factor easily, so you can use the quadratic equation;<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=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=5x%5E2%2B-44x%2B80+=+0 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-44x%2B80+=+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=%28-44%29%5E2-4%2A5%2A80=336 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-44%29%5E2-4%2A5%2A80=336\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=336 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--44%2B-sqrt%28+336+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--44%2B-sqrt%28+336+%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-%28-44%29%2Bsqrt%28+336+%29%29%2F2%5C5+=+6.23303027798234 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-44%29%2Bsqrt%28+336+%29%29%2F2%5C5+=+6.23303027798234\"   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-%28-44%29-sqrt%28+336+%29%29%2F2%5C5+=+2.56696972201766 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-44%29-sqrt%28+336+%29%29%2F2%5C5+=+2.56696972201766\"   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=5x%5E2%2B-44x%2B80 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-44x%2B80\"   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=5x%5E2%2B-44x%2B80+=+5%28x-6.23303027798234%29%2A%28x-2.56696972201766%29 ALIGN=MIDDLE  ALT=\"5x%5E2%2B-44x%2B80+=+5%28x-6.23303027798234%29%2A%28x-2.56696972201766%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.23303027798234, 2.56696972201766.\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+5%2Ax%5E2%2B-44%2Ax%2B80+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-44%2Ax%2B80+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );