document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124675>Question 124675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve. \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 #91380 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91380\">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=sqrt%28x-1%29%2Bsqrt%28x-4%29=sqrt%282x-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-1%29%2Bsqrt%28x-4%29=sqrt%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x-1%29%2Bsqrt%28x-4%29%29%5E2=%28sqrt%282x-1%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28x-1%29%2Bsqrt%28x-4%29%29%5E2=%28sqrt%282x-1%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28x-1%29%2Bsqrt%28x-4%29%29%5E2=2x-1 ALIGN=MIDDLE  ALT=\"%28sqrt%28x-1%29%2Bsqrt%28x-4%29%29%5E2=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square the right side to remove the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-1%29sqrt%28x-1%29%2B2sqrt%28x-1%29sqrt%28x-4%29%2Bsqrt%28x-4%29sqrt%28x-4%29=2x-1 ALIGN=MIDDLE  ALT=\"sqrt%28x-1%29sqrt%28x-1%29%2B2sqrt%28x-1%29sqrt%28x-4%29%2Bsqrt%28x-4%29sqrt%28x-4%29=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2B2sqrt%28%28x-1%29%28x-4%29%29%2B%28x-4%29=2x-1 ALIGN=MIDDLE  ALT=\"%28x-1%29%2B2sqrt%28%28x-1%29%28x-4%29%29%2B%28x-4%29=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2B2sqrt%28x%5E2-5x%2B4%29%2B%28x-4%29=2x-1 ALIGN=MIDDLE  ALT=\"%28x-1%29%2B2sqrt%28x%5E2-5x%2B4%29%2B%28x-4%29=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-5%2B2sqrt%28x%5E2-5x%2B4%29=2x-1 ALIGN=MIDDLE  ALT=\"2x-5%2B2sqrt%28x%5E2-5x%2B4%29=2x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28x%5E2-5x%2B4%29=2x-1-2x%2B5 ALIGN=MIDDLE  ALT=\"2sqrt%28x%5E2-5x%2B4%29=2x-1-2x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 2x from both sides. Add 5 to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28x%5E2-5x%2B4%29=4 ALIGN=MIDDLE  ALT=\"2sqrt%28x%5E2-5x%2B4%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2-5x%2B4%29=2 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2-5x%2B4%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x%2B4=4 ALIGN=MIDDLE  ALT=\"x%5E2-5x%2B4=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-5x=0 ALIGN=MIDDLE  ALT=\"x%5E2-5x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Subtract 4 from both sides. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-5%29=0 ALIGN=MIDDLE  ALT=\"x%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the left side \r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=0 ALIGN=MIDDLE  ALT=\"x-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Now solve for x in each case\r<BR>\n" );
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document.write( "So our possible answers are:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Let's verify the first solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-1%29%2Bsqrt%28x-4%29=sqrt%282x-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-1%29%2Bsqrt%28x-4%29=sqrt%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280-1%29%2Bsqrt%280-4%29=sqrt%282%280%29-1%29 ALIGN=MIDDLE  ALT=\"sqrt%280-1%29%2Bsqrt%280-4%29=sqrt%282%280%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-1%29%2Bsqrt%28-4%29=sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28-1%29%2Bsqrt%28-4%29=sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%2B2i=i ALIGN=MIDDLE  ALT=\"i%2B2i=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3i=i ALIGN=MIDDLE  ALT=\"3i=i\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add.  Since the two sides of the equation are <b>not</b> equal, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <b>not</b> a solution.\r<BR>\n" );
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document.write( "Let's verify the second solution <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-1%29%2Bsqrt%28x-4%29=sqrt%282x-1%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-1%29%2Bsqrt%28x-4%29=sqrt%282x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285-1%29%2Bsqrt%285-4%29=sqrt%282%285%29-1%29 ALIGN=MIDDLE  ALT=\"sqrt%285-1%29%2Bsqrt%285-4%29=sqrt%282%285%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%29%2Bsqrt%281%29=sqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%284%29%2Bsqrt%281%29=sqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B1=3 ALIGN=MIDDLE  ALT=\"2%2B1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=3 ALIGN=MIDDLE  ALT=\"3=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add.  Since the two sides of the equation are equal, this verifies the solution\r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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