document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885126>Question 885126</A>: <I><SPAN STYLE=\"word-break: break-all;\">  \log_(5) (x) + \log_(5) (x+5) = 9 \r<BR>\n" );
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document.write( "I need help solving for x.  I keep getting crazy numbers.<BR>\n" );
document.write( "Because I have base 5, I set up my equation as <BR>\n" );
document.write( "5^9 = x(x+5)<BR>\n" );
document.write( "1953125 = x^2 +5x<BR>\n" );
document.write( "x^2 + 5x - 1953125 = 0\r<BR>\n" );
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document.write( "I couldn't factor it and the quadratic formula didnt seem to work either.  Please help!  Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534940 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=534940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> log_(5) (x) + log_(5) (x+5) = 9 <BR>\n" );
document.write( "log_(5) [(x)(x+5)] = 9 <BR>\n" );
document.write( "(x)(x+5) = 5^9 <BR>\n" );
document.write( "x^2+5x = 1953125 <BR>\n" );
document.write( "x^2+5x-1953125 = 0<BR>\n" );
document.write( "apply the \"quadratic\" formula:<BR>\n" );
document.write( "x = -b+-sqrt(b^2-4ac)/(2a)<BR>\n" );
document.write( "to get:<BR>\n" );
document.write( "x = {1395.04, -1400.04}<BR>\n" );
document.write( "throw out the negative solution (extraneous) to get<BR>\n" );
document.write( "x = 1395.04<BR>\n" );
document.write( ".<BR>\n" );
document.write( "details of quadratic follows:<BR>\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=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=1x%5E2%2B5x%2B-1953125+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-1953125+=+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=%285%29%5E2-4%2A1%2A-1953125=7812525 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%285%29%5E2-4%2A1%2A-1953125=7812525\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=7812525 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+=+%28-5%2B-sqrt%28+7812525+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-5%2B-sqrt%28+7812525+%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-%285%29%2Bsqrt%28+7812525+%29%29%2F2%5C1+=+1395.04472200356 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%285%29%2Bsqrt%28+7812525+%29%29%2F2%5C1+=+1395.04472200356\"   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-%285%29-sqrt%28+7812525+%29%29%2F2%5C1+=+-1400.04472200356 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%285%29-sqrt%28+7812525+%29%29%2F2%5C1+=+-1400.04472200356\"   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%2B5x%2B-1953125 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-1953125\"   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%2B5x%2B-1953125+=+1%28x-1395.04472200356%29%2A%28x--1400.04472200356%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B5x%2B-1953125+=+1%28x-1395.04472200356%29%2A%28x--1400.04472200356%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1395.04472200356, -1400.04472200356.\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%2B5%2Ax%2B-1953125+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-1953125+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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