document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198474>Question 198474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi!\r<BR>\n" );
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document.write( "Solve the equation (1+sqrt(x))^2-2(1+sqrt(x))-15=0\r<BR>\n" );
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document.write( "thanks!\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 #148996 by </B><A HREF=/tutors/aboutme.mpl?userid=MRperkins><B>MRperkins(300)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MRperkins><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=MRperkins><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is probably more than one way to solve this, but the easiest way is actually quite easy and I am sure you will understand it once we are done.  <BR>\n" );
document.write( "First, notice that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsqrt%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2Bsqrt%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the second term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2A%281%2Bsqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"-2%2A%281%2Bsqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, select any variable to replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%28x%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > let's say z<BR>\n" );
document.write( "so now substitute z for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%28x%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you get a problem that you better understand which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2-2z-15=0 ALIGN=MIDDLE  ALT=\"z%5E2-2z-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you can factor the problem to factors of 15 that subtract and give you -2 which are -5 and 2<BR>\n" );
document.write( "so you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28z-5%29%28z%2B2%29=0 ALIGN=MIDDLE  ALT=\"%28z-5%29%28z%2B2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means either z-5=0 or z+2=0<BR>\n" );
document.write( "so z=5 or z=-2\r<BR>\n" );
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document.write( "Substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%28x%29 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for z and you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%28x%29=5 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%28x%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Bsqrt%28x%29=-2 ALIGN=MIDDLE  ALT=\"1%2Bsqrt%28x%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29=4 ALIGN=MIDDLE  ALT=\"sqrt%28x%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29=-3 ALIGN=MIDDLE  ALT=\"sqrt%28x%29=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "square both sides and you get<BR>\n" );
document.write( "x=16 and x=9\r<BR>\n" );
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document.write( "check your answers by plugging in your answers<BR>\n" );
document.write( "1.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsqrt%2816%29%29%5E2-2%281%2Bsqrt%2816%29%29-15=0 ALIGN=MIDDLE  ALT=\"%281%2Bsqrt%2816%29%29%5E2-2%281%2Bsqrt%2816%29%29-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B4%29%5E2-2%285%29-15=0 ALIGN=MIDDLE  ALT=\"%281%2B4%29%5E2-2%285%29-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25-10-15=0 ALIGN=MIDDLE  ALT=\"25-10-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  0=0 so 16 does work!\r<BR>\n" );
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document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Bsqrt%289%29%29%5E2-2%281%2Bsqrt%289%29%29-15=0 ALIGN=MIDDLE  ALT=\"%281%2Bsqrt%289%29%29%5E2-2%281%2Bsqrt%289%29%29-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B3%29%5E2-2%281%2B3%29-15=0 ALIGN=MIDDLE  ALT=\"%281%2B3%29%5E2-2%281%2B3%29-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16-8-15=0 ALIGN=MIDDLE  ALT=\"16-8-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -7 does not equal 0 so 9 does not work.  Therefore, your only real answer is x=16\r<BR>\n" );
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document.write( "I hope this helps!<BR>\n" );
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