document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174686>Question 174686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i solve the quadratic equasion x^2+11x-80=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129733 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I like to use the method called \"completing the square\"<BR>\n" );
document.write( "To do this you first get the constant term on the <BR>\n" );
document.write( "other side<BR>\n" );
document.write( "(1) Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+11x+-+80+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+11x+-+80+=+0\"   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+%2B+11x+=+80 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+11x+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) Now divide the coefficient of the x term by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "then square it and add this to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+11x+%2B+%2811%2F2%29%5E2+=+80+%2B+%2811%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+11x+%2B+%2811%2F2%29%5E2+=+80+%2B+%2811%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The purpose of this is to make the left side a perfect<BR>\n" );
document.write( "square, which it is. It might be hard to see, but I<BR>\n" );
document.write( "can rewrite this as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+11%2F2%29%5E2+=+80+%2B+%2811%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+%2B+11%2F2%29%5E2+=+80+%2B+%2811%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I want to express <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=320%2F4 ALIGN=MIDDLE  ALT=\"320%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+11%2F2%29%5E2+=+320%2F4+%2B+121%2F4 ALIGN=MIDDLE  ALT=\"%28x+%2B+11%2F2%29%5E2+=+320%2F4+%2B+121%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+11%2F2%29%5E2+=+441%2F4 ALIGN=MIDDLE  ALT=\"%28x+%2B+11%2F2%29%5E2+=+441%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now take the square root of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+11%2F2+=+0+%2B-sqrt%28441%29%2F2 ALIGN=MIDDLE  ALT=\"x+%2B+11%2F2+=+0+%2B-sqrt%28441%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+%2B+21%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-11+%2B+21%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-11+-+21%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%28-11+-+21%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-16 ALIGN=MIDDLE  ALT=\"x+=+-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "check answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+11x+-+80+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+11x+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2+%2B+11%2A5+-+80+=+0 ALIGN=MIDDLE  ALT=\"5%5E2+%2B+11%2A5+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+%2B+55+-+80+=+0 ALIGN=MIDDLE  ALT=\"25+%2B+55+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+0 ALIGN=MIDDLE  ALT=\"0+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16%29%5E2+%2B+11%2A%28-16%29+-+80+=+0 ALIGN=MIDDLE  ALT=\"%28-16%29%5E2+%2B+11%2A%28-16%29+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256+-+176+-+80+=+0 ALIGN=MIDDLE  ALT=\"256+-+176+-+80+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=256+-+256+=+0 ALIGN=MIDDLE  ALT=\"256+-+256+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+0 ALIGN=MIDDLE  ALT=\"0+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );