document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109273>Question 1109273</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help. Can't solve it.\r<BR>\n" );
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document.write( "3.25(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2))=50000\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724270 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I need help. Can't solve it.\r<BR>\n" );
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document.write( "3.25(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2))=50000<BR>\n" );
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document.write( "It's just a matter of being careful.\r<BR>\n" );
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document.write( "13(48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2)) = 200000<BR>\n" );
document.write( "48x+x(x/6)+2x*sqrt((x/2)^2+(x/6)^2) = 200000/13<BR>\n" );
document.write( "48x + x^2/6 + 2x*sqrt((x^2/4 + (x^2/36)) = 200000/13<BR>\n" );
document.write( "48x + x^2/6 + 2x*sqrt((10x^2/36)) = 200000/13<BR>\n" );
document.write( "48x + x^2/6 + 2x*(x/6)sqrt(10) = 200000/13<BR>\n" );
document.write( "48x + x^2/6 + (x^2/3)sqrt(10) = 200000/13<BR>\n" );
document.write( "x^2/6 + (2x^2/6)sqrt(10) + 48x = 200000/13<BR>\n" );
document.write( "x^2*(2sqrt(10)+1)/6 + 48x - 200000/13 = 0<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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=1.22075922005613x%5E2%2B48x%2B-15384.6153846154+=+0 ALIGN=MIDDLE  ALT=\"1.22075922005613x%5E2%2B48x%2B-15384.6153846154+=+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=%2848%29%5E2-4%2A1.22075922005613%2A-15384.6153846154=77427.6443111465 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2848%29%5E2-4%2A1.22075922005613%2A-15384.6153846154=77427.6443111465\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=77427.6443111465 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+=+%28-48%2B-sqrt%28+77427.6443111465+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-48%2B-sqrt%28+77427.6443111465+%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-%2848%29%2Bsqrt%28+77427.6443111465+%29%29%2F2%5C1.22075922005613+=+94.3094384866179 ALIGN=MIDDLE   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-%2848%29-sqrt%28+77427.6443111465+%29%29%2F2%5C1.22075922005613+=+-133.629231621412 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.22075922005613x%5E2%2B48x%2B-15384.6153846154 ALIGN=MIDDLE  ALT=\"1.22075922005613x%5E2%2B48x%2B-15384.6153846154\"   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=1.22075922005613x%5E2%2B48x%2B-15384.6153846154+=+%28x-94.3094384866179%29%2A%28x--133.629231621412%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 94.3094384866179, -133.629231621412.\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+1.22075922005613%2Ax%5E2%2B48%2Ax%2B-15384.6153846154+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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