document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012127>Question 1012127</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening (Happy New Year to you all!!)<BR>\n" );
document.write( "Has somebody the patience to explain me step by step the solution of<BR>\n" );
document.write( "this exp.equation:?  4^(x-3)+2^(13-2x)=24 <BR>\n" );
document.write( "Results should be: x=9/2 or x=5 <BR>\n" );
document.write( "Thank you very much in advance<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627977 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=627977\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 4^(x-3)+2^(13-2x)=24<BR>\n" );
document.write( "4 = 2^2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282x-6%29+%2B+2%5E%2813-2x%29+=+24 ALIGN=MIDDLE  ALT=\"2%5E%282x-6%29+%2B+2%5E%2813-2x%29+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282x%29%2F2%5E6+%2B+2%5E13%2F%282%5E%282x%29%29+=+24 ALIGN=MIDDLE  ALT=\"2%5E%282x%29%2F2%5E6+%2B+2%5E13%2F%282%5E%282x%29%29+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282x%29%2A2%5E%282x%29+%2B+2%5E13%2A2%5E6+=+24%2A2%5E6%2A2%5E%282x%29 ALIGN=MIDDLE  ALT=\"2%5E%282x%29%2A2%5E%282x%29+%2B+2%5E13%2A2%5E6+=+24%2A2%5E6%2A2%5E%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%284x%29+-+24%2A64%2A2%5E%282x%29+%2B+2%5E19+=+0 ALIGN=MIDDLE  ALT=\"2%5E%284x%29+-+24%2A64%2A2%5E%282x%29+%2B+2%5E19+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sub u for 2^2x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2+-+1536u+%2B+2%5E19+=+0 ALIGN=MIDDLE  ALT=\"u%5E2+-+1536u+%2B+2%5E19+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=1x%5E2%2B-1536x%2B524288+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1536x%2B524288+=+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=%28-1536%29%5E2-4%2A1%2A524288=262144 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1536%29%5E2-4%2A1%2A524288=262144\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=262144 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--1536%2B-sqrt%28+262144+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1536%2B-sqrt%28+262144+%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-%28-1536%29%2Bsqrt%28+262144+%29%29%2F2%5C1+=+1024 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1536%29%2Bsqrt%28+262144+%29%29%2F2%5C1+=+1024\"   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-%28-1536%29-sqrt%28+262144+%29%29%2F2%5C1+=+512 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1536%29-sqrt%28+262144+%29%29%2F2%5C1+=+512\"   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-1536x%2B524288 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1536x%2B524288\"   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-1536x%2B524288+=+%28x-1024%29%2A%28x-512%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1536x%2B524288+=+%28x-1024%29%2A%28x-512%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1024, 512.\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-1536%2Ax%2B524288+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1536%2Ax%2B524288+%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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282x%29+=+1024+=+2%5E10 ALIGN=MIDDLE  ALT=\"2%5E%282x%29+=+1024+=+2%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2x = 10<BR>\n" );
document.write( "x = 5<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E%282x%29+=+512+=+2%5E9 ALIGN=MIDDLE  ALT=\"2%5E%282x%29+=+512+=+2%5E9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 9/2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );