document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177079>Question 177079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm trying to help my granddaughter.  I'm stumped\r<BR>\n" );
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document.write( "p-4/9p = -7/9 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #132103 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=132103\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think you mean:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-4%29%2F9p+=+-7%2F9 ALIGN=MIDDLE  ALT=\"%28p-4%29%2F9p+=+-7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by 9p:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p-4%29+=+-7p ALIGN=MIDDLE  ALT=\"%28p-4%29+=+-7p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 7p to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6p-4+=+0 ALIGN=MIDDLE  ALT=\"6p-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 4 to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6p+=+4 ALIGN=MIDDLE  ALT=\"6p+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by 6:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+4%2F6 ALIGN=MIDDLE  ALT=\"p+=+4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "reduce to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+2%2F3 ALIGN=MIDDLE  ALT=\"p+=+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "BUT, if you mean:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p-4%2F9p+=+-7%2F9 ALIGN=MIDDLE  ALT=\"p-4%2F9p+=+-7%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by 9p:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p%5E2-4+=+-7p+ ALIGN=MIDDLE  ALT=\"9p%5E2-4+=+-7p+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add 7p to both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p%5E2%2B7p-4+=+0+ ALIGN=MIDDLE  ALT=\"9p%5E2%2B7p-4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here, you have to use the quadratic equation to solve.<BR>\n" );
document.write( "Doing so will yield:<BR>\n" );
document.write( "p = {0.383, -1.161}<BR>\n" );
document.write( "Details are below:<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=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=ap%5E2%2Bbp%2Bc=0 ALIGN=MIDDLE  ALT=\"ap%5E2%2Bbp%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9p%5E2%2B7p%2B-4+=+0 ALIGN=MIDDLE  ALT=\"9p%5E2%2B7p%2B-4+=+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=p%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"p%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=%287%29%5E2-4%2A9%2A-4=193 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%287%29%5E2-4%2A9%2A-4=193\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=193 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+=+%28-7%2B-sqrt%28+193+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-7%2B-sqrt%28+193+%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=p%5B1%5D+=+%28-%287%29%2Bsqrt%28+193+%29%29%2F2%5C9+=+0.382913554969434 ALIGN=MIDDLE  ALT=\"p%5B1%5D+=+%28-%287%29%2Bsqrt%28+193+%29%29%2F2%5C9+=+0.382913554969434\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5B2%5D+=+%28-%287%29-sqrt%28+193+%29%29%2F2%5C9+=+-1.16069133274721 ALIGN=MIDDLE  ALT=\"p%5B2%5D+=+%28-%287%29-sqrt%28+193+%29%29%2F2%5C9+=+-1.16069133274721\"   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=9p%5E2%2B7p%2B-4 ALIGN=MIDDLE  ALT=\"9p%5E2%2B7p%2B-4\"   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=9p%5E2%2B7p%2B-4+=+9%28p-0.382913554969434%29%2A%28p--1.16069133274721%29 ALIGN=MIDDLE  ALT=\"9p%5E2%2B7p%2B-4+=+9%28p-0.382913554969434%29%2A%28p--1.16069133274721%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.382913554969434, -1.16069133274721.\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+9%2Ax%5E2%2B7%2Ax%2B-4+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B7%2Ax%2B-4+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( ".<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );