document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82632>Question 82632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a real difficulty in figuring out how to solve these exponential equations. Your help is greatly appreciated.<BR>\n" );
document.write( "Solve each exponential equation. Give answers to four decimal places when necessary:\r<BR>\n" );
document.write( "\n" );
document.write( "2^x^2-2x =8 and 3^x^2+4x = 1/81 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59282 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=59282\">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=2%5Ex%5E2+-+2x+=+8 ALIGN=MIDDLE  ALT=\"2%5Ex%5E2+-+2x+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5Ex%5E2+%2B+4x+=+1%2F81 ALIGN=MIDDLE  ALT=\"3%5Ex%5E2+%2B+4x+=+1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the 1st one,<BR>\n" );
document.write( "subtract 8 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+-+2x+-8+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+-+2x+-8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+-+4+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+-+4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The easiest way is to complete the square<BR>\n" );
document.write( "Take half the coefficient of x, square it, then add that<BR>\n" );
document.write( "to both sides<BR>\n" );
document.write( "To set it up, I'll add 4 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+=+4 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-1%29+%2F+2%29%5E2+=+1%2F4 ALIGN=MIDDLE  ALT=\"%28%28-1%29+%2F+2%29%5E2+=+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > add this to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+%2B+1%2F4+=+4+%2B+1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+%2B+1%2F4+=+4+%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice the left side is a perfect square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%2F2%29%5E2+=+17%2F4 ALIGN=MIDDLE  ALT=\"%28x+-+1%2F2%29%5E2+=+17%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Take the sqrt of both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+1%2F2+=+%2817%29%5E%281%2F2%29+%2F+2 ALIGN=MIDDLE  ALT=\"x+-+1%2F2+=+%2817%29%5E%281%2F2%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%2817%29%5E%281%2F2%29%2B+1%29+%2F+2 ALIGN=MIDDLE  ALT=\"x+=+%28%2817%29%5E%281%2F2%29%2B+1%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can check this by plugging it back into the equation for x<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2+%2B+4x+=+1%2F81 ALIGN=MIDDLE  ALT=\"3x%5E2+%2B+4x+=+1%2F81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%284%2F3%29x+=+1%2F3%2A81 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%284%2F3%29x+=+1%2F3%2A81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complete the square again<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%284%2F3%29x+%2B+4%2F9+=+1%2F3%2A81+%2B+4%2F9 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%284%2F3%29x+%2B+4%2F9+=+1%2F3%2A81+%2B+4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%284%2F3%29x+%2B+4%2F9+=+%281+%2B+27%2A4%29+%2F+3%2A81 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%284%2F3%29x+%2B+4%2F9+=+%281+%2B+27%2A4%29+%2F+3%2A81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%282%2F3%29%29%5E2+=+109+%2F+243 ALIGN=MIDDLE  ALT=\"x+%2B+%282%2F3%29%29%5E2+=+109+%2F+243\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+%282%2F3%29+=+%28109%2F243%29%5E%281%2F2%29 ALIGN=MIDDLE  ALT=\"x+%2B+%282%2F3%29+=+%28109%2F243%29%5E%281%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28109%2F243%29%5E%281%2F2%29+-+%282%2F3%29 ALIGN=MIDDLE  ALT=\"x+=+%28109%2F243%29%5E%281%2F2%29+-+%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I could have made a mistake, but that's the method </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );