document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=431405>Question 431405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a number minus the ^2 of the number = 2/9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299403 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=299403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a number minus the ^2 of the number = 2/9<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let x = the number<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+-+x%5E2+=+2%2F9%29%0D%0A%7B%7B%7B+x++=+x%5E2+%2B+2%2F9%29%0D%0A%7B%7B%7B+0++=+x%5E2+-+x+%2B+2%2F9%29%0D%0Aapplying+the+quadratic+formula+we+get%3A%0D%0Ax+=+%7B0.667%2C+0.333%7D%0D%0A.%0D%0ADetails+of+quadratic+solution+follows%3A%0D%0A%3CTABLE+BORDER=1%3E%0A+%3CTR%3E%3CTD+ALIGN=MIDDLE%3ESolved+by+%3CA+ rel=nofollow HREF=http%3A%2F%2Fwiki.algebra.com%2Findex.php%2FTutoring_-_pluggable_solvers%3Epluggable%3C%2FA%3E+solver%3A+%3CA+ rel=nofollow HREF=quadratic.solver%3ESOLVE+quadratic+equation+with+variable%3C%2FA%3E%3C%2FTD%3E%3C%2FTR%3E%0A%3CTR%3E%3CTD+ALIGN=LEFT%3EQuadratic+equation+%7B%7B%7Bax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-1x%2B0.222222222222222+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B0.222222222222222+=+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=%28-1%29%5E2-4%2A1%2A0.222222222222222=0.111111111111112 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1%29%5E2-4%2A1%2A0.222222222222222=0.111111111111112\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=0.111111111111112 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--1%2B-sqrt%28+0.111111111111112+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1%2B-sqrt%28+0.111111111111112+%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-%28-1%29%2Bsqrt%28+0.111111111111112+%29%29%2F2%5C1+=+0.666666666666667 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+0.111111111111112+%29%29%2F2%5C1+=+0.666666666666667\"   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-%28-1%29-sqrt%28+0.111111111111112+%29%29%2F2%5C1+=+0.333333333333333 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1%29-sqrt%28+0.111111111111112+%29%29%2F2%5C1+=+0.333333333333333\"   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=1x%5E2%2B-1x%2B0.222222222222222 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B0.222222222222222\"   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=1x%5E2%2B-1x%2B0.222222222222222+=+1%28x-0.666666666666667%29%2A%28x-0.333333333333333%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B0.222222222222222+=+1%28x-0.666666666666667%29%2A%28x-0.333333333333333%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.666666666666667, 0.333333333333333.\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+1%2Ax%5E2%2B-1%2Ax%2B0.222222222222222+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B0.222222222222222+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR></TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );