document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086139>Question 1086139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a and x satisfy x^2 + (a-(1/a))x - 1 = 0. Solve for x in terms of a.\r<BR>\n" );
document.write( "\n" );
document.write( "*That's a quadratic in x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700302 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=700302\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use a substitution for ease,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=a-1%2Fa ALIGN=MIDDLE  ALT=\"C=a-1%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complete the square,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2BCx-1=0 ALIGN=MIDDLE  ALT=\"x%5E2%2BCx-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2BCx%2B%28C%2F2%29%5E2%29=1%2B%28C%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%2BCx%2B%28C%2F2%29%5E2%29=1%2B%28C%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2BC%2F2%29%5E2=1%2BC%5E2%2F4 ALIGN=MIDDLE  ALT=\"%28x%2BC%2F2%29%5E2=1%2BC%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2BC%2F2=0+%2B-+sqrt%28%284%2BC%5E2%29%2F4%29 ALIGN=MIDDLE  ALT=\"x%2BC%2F2=0+%2B-+sqrt%28%284%2BC%5E2%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-C%2F2+%2B-+sqrt%284%2BC%5E2%29%2F2 ALIGN=MIDDLE  ALT=\"x=-C%2F2+%2B-+sqrt%284%2BC%5E2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2F2=a%2F2-1%2F%282a%29 ALIGN=MIDDLE  ALT=\"C%2F2=a%2F2-1%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2F2=a%5E2%2F%282a%29-1%2F%282a%29 ALIGN=MIDDLE  ALT=\"C%2F2=a%5E2%2F%282a%29-1%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2F2=%28a%5E2-1%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"C%2F2=%28a%5E2-1%29%2F%282a%29\"   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=C=%28a%5E2-1%29%2Fa ALIGN=MIDDLE  ALT=\"C=%28a%5E2-1%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5E2=%28a%5E2-1%29%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"C%5E2=%28a%5E2-1%29%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2BC%5E2=4a%5E2%2Fa%5E2%2B%28a%5E2-1%29%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"4%2BC%5E2=4a%5E2%2Fa%5E2%2B%28a%5E2-1%29%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2BC%5E2=%284a%5E2%2B%28a%5E2-1%29%5E2%29%2Fa%5E2 ALIGN=MIDDLE  ALT=\"4%2BC%5E2=%284a%5E2%2B%28a%5E2-1%29%5E2%29%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2BC%5E2=%284a%5E2%2Ba%5E4-2a%5E2%2B1%29%2Fa%5E2 ALIGN=MIDDLE  ALT=\"4%2BC%5E2=%284a%5E2%2Ba%5E4-2a%5E2%2B1%29%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2BC%5E2=%28a%5E4%2B2a%5E2%2B1%29%2Fa%5E2 ALIGN=MIDDLE  ALT=\"4%2BC%5E2=%28a%5E4%2B2a%5E2%2B1%29%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2BC%5E2=%28a%5E2%2B1%29%5E2%2Fa%5E2 ALIGN=MIDDLE  ALT=\"4%2BC%5E2=%28a%5E2%2B1%29%5E2%2Fa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=-C+%2B-+sqrt%284%2BC%5E2%29 ALIGN=MIDDLE  ALT=\"2x=-C+%2B-+sqrt%284%2BC%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=%281-a%5E2%29%2Fa+%2B-+sqrt%28%28a%5E2%2B1%29%5E2%2Fa%5E2%29 ALIGN=MIDDLE  ALT=\"2x=%281-a%5E2%29%2Fa+%2B-+sqrt%28%28a%5E2%2B1%29%5E2%2Fa%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x=%281-a%5E2%29%2Fa+%2B-+%28a%5E2%2B1%29%2Fa ALIGN=MIDDLE  ALT=\"2x=%281-a%5E2%29%2Fa+%2B-+%28a%5E2%2B1%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xa=1-a%5E2+%2B-+%28a%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"2xa=1-a%5E2+%2B-+%28a%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\"Positive\" solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xa=1-a%5E2+%2B+a%5E2%2B1 ALIGN=MIDDLE  ALT=\"2xa=1-a%5E2+%2B+a%5E2%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xa=2 ALIGN=MIDDLE  ALT=\"2xa=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=1%2Fa%29 ALIGN=MIDDLE  ALT=\"highlight%28x=1%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\"Negative\" solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xa=1-a%5E2+-+a%5E2-1%29 ALIGN=MIDDLE  ALT=\"2xa=1-a%5E2+-+a%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xa=-2a%5E2 ALIGN=MIDDLE  ALT=\"2xa=-2a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-a%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );