document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051558>Question 1051558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following equation.<BR>\n" );
document.write( "1/5 r^(3/2) + 5/2 r^(1/2) =0. Thanks a lot! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #667016 by </B><A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><B>advanced_Learner(501)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=advanced_Learner><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=advanced_Learner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=667016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F5%29%2Ar%5E%283%2F2%29%2B%285%2F2%29%2Ar%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%281%2F5%29%2Ar%5E%283%2F2%29%2B%285%2F2%29%2Ar%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2Ar%5E%283%2F2%29%2B%2825%29%2Ar%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"%282%29%2Ar%5E%283%2F2%29%2B%2825%29%2Ar%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2AS%5E%283%29%2B%2825%29%2AS ALIGN=MIDDLE  ALT=\"%282%29%2AS%5E%283%29%2B%2825%29%2AS\"   DISABLED_style= \"max-width:90%; height:auto;\" >=0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28%282%29%2AS%5E%282%29%2B%2825%29%29 ALIGN=MIDDLE  ALT=\"S%28%282%29%2AS%5E%282%29%2B%2825%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=0\r<BR>\n" );
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document.write( "first case s=0 meaning r=0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2AS%5E%282%29%2B%2825%29 ALIGN=MIDDLE  ALT=\"%282%29%2AS%5E%282%29%2B%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=0\r<BR>\n" );
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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=aS%5E2%2BbS%2Bc=0 ALIGN=MIDDLE  ALT=\"aS%5E2%2BbS%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2S%5E2%2B0S%2B25+=+0 ALIGN=MIDDLE  ALT=\"2S%5E2%2B0S%2B25+=+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=S%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"S%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=%280%29%5E2-4%2A2%2A25=-200 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%280%29%5E2-4%2A2%2A25=-200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -200 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -200 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+200%29+=+14.142135623731 ALIGN=MIDDLE  ALT=\"sqrt%28+200%29+=+14.142135623731\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B12%5D+=+%28-0%2B-+i%2Asqrt%28+-200+%29%29%2F2%5C2+=++%28-0%2B-+i%2A14.142135623731%29%2F2%5C2+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\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+2%2Ax%5E2%2B0%2Ax%2B25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B0%2Ax%2B25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );