document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=753630>Question 753630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find x, if;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%285%2B2sqrt2%29%5E%28x%5E2-x%29+%2B+%285-2sqrt2%29%5E%28x%5E2-x%29+=10++ ALIGN=MIDDLE  ALT=\"+%285%2B2sqrt2%29%5E%28x%5E2-x%29+%2B+%285-2sqrt2%29%5E%28x%5E2-x%29+=10++\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #458572 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=458572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29=%285%2B2sqrt%282%29%29%5Ey%2B%285-2sqrt%282%29%29%5Ey ALIGN=MIDDLE  ALT=\"g%28y%29=%285%2B2sqrt%282%29%29%5Ey%2B%285-2sqrt%282%29%29%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%281%29=%285%2B2sqrt%282%29%29%5E1%2B%285-2sqrt%282%29%29%5E1=5%2B2sqrt%282%29%2B5-2sqrt%282%29=10 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29=%285%2B2sqrt2%29%5Ey%2B%285-2sqrt2%29%5Ey ALIGN=MIDDLE  ALT=\"g%28y%29=%285%2B2sqrt2%29%5Ey%2B%285-2sqrt2%29%5Ey\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the sum of two exponential functions,<BR>\n" );
document.write( "with positive bases, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%3C5-2sqrt2%3C5%2B2sqrt2 ALIGN=MIDDLE  ALT=\"0%3C5-2sqrt2%3C5%2B2sqrt2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Those two exponmential functions, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29 ALIGN=MIDDLE  ALT=\"g%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, increase with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > throughout their real numbers domain, from -infinity to infinity.<BR>\n" );
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document.write( "So for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C1 ALIGN=MIDDLE  ALT=\"y%3C1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29%3C10 ALIGN=MIDDLE  ALT=\"g%28y%29%3C10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E1 ALIGN=MIDDLE  ALT=\"y%3E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29%3E10 ALIGN=MIDDLE  ALT=\"g%28y%29%3E10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The only value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > that makes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28y%29=10 ALIGN=MIDDLE  ALT=\"g%28y%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1 ALIGN=MIDDLE  ALT=\"y=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then, the only solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B2sqrt%282%29%29%5E%28x%5E2-x%29%2B%285-2sqrt%282%29%29%5E%28x%5E2-x%29=10 ALIGN=MIDDLE  ALT=\"%285%2B2sqrt%282%29%29%5E%28x%5E2-x%29%2B%285-2sqrt%282%29%29%5E%28x%5E2-x%29=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "will be the solutions of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x=1 ALIGN=MIDDLE  ALT=\"x%5E2-x=1\"   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%5E2-x=1 ALIGN=MIDDLE  ALT=\"x%5E2-x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-1=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Applying the quadratic formula, we find<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1+%2B-+sqrt%281%5E2-4%281%29%28-1%29%29%29%2F2%2F1 ALIGN=MIDDLE  ALT=\"x=%28-1+%2B-+sqrt%281%5E2-4%281%29%28-1%29%29%29%2F2%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=%281+%2B-+sqrt%285%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=%281+%2B-+sqrt%285%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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