document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=51968>Question 51968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not sure if I am getting the right answer for this problem.  I need a little help.\r<BR>\n" );
document.write( "\n" );
document.write( "For the equation x - the square root of x = 0, perform the following:<BR>\n" );
document.write( " 	Solve for all values of x that satisfies the equation\r<BR>\n" );
document.write( "\n" );
document.write( "Graph the functions y = x and y = the square root of x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.\r<BR>\n" );
document.write( "\n" );
document.write( "I am not sure how to graph this function.  Thanks for your time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34663 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=34663\">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=x-sqrt%28x%29=0 ALIGN=MIDDLE  ALT=\"x-sqrt%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  can be solved algebraically a couple of different ways.  I showed another student one way to solve it earlier today.  Look it up and I'll show you a second way to do it.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-sqrt%28x%29=0 ALIGN=MIDDLE  ALT=\"x-sqrt%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-sqrt%28x%29%2Bsqrt%28x%29=0%2Bsqrt%28x%29 ALIGN=MIDDLE  ALT=\"x-sqrt%28x%29%2Bsqrt%28x%29=0%2Bsqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (simplify)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%5E2=%28sqrt%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%29%5E2=%28sqrt%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (square both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=x ALIGN=MIDDLE  ALT=\"x%5E2=x\"   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-x=x-x ALIGN=MIDDLE  ALT=\"x%5E2-x=x-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (subtract x from both sides)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-1%29=0 ALIGN=MIDDLE  ALT=\"x%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >     (factor out an x)<BR>\n" );
document.write( "x=0 and x-1=0 (zero product property)<BR>\n" );
document.write( "x=0 and x-1+1=0+1 <BR>\n" );
document.write( "x=0 and x=1<BR>\n" );
document.write( "Because this involves a square root you'll need to check for false solutions called extraneous solutions by substituting the answers back into the original equations to make sure they work.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%29-sqrt%280%29=0 ALIGN=MIDDLE  ALT=\"%280%29-sqrt%280%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "0-0=0 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29-sqrt%281%29=0 ALIGN=MIDDLE  ALT=\"%281%29-sqrt%281%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1-1=0<BR>\n" );
document.write( "Both x=0 and x=1 are valid solutions.<BR>\n" );
document.write( "As for the graphing:<BR>\n" );
document.write( "y=x is a line, you can substitute values for x and get coordinates for points to connect.<BR>\n" );
document.write( "When x=0, y=0 gives you the coordinate  (0,0)<BR>\n" );
document.write( "When x =1, y=1   (1,1)<BR>\n" );
document.write( "When x=2, y=2    (2,2)<BR>\n" );
document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When x=0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%280%29 ALIGN=MIDDLE  ALT=\"y=sqrt%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "          y=0    (0,0)<BR>\n" );
document.write( "When x=1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%281%29 ALIGN=MIDDLE  ALT=\"y=sqrt%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "          y=1    (1,1)<BR>\n" );
document.write( "When x=4, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%284%29 ALIGN=MIDDLE  ALT=\"y=sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "          y=2    (4,2)\r<BR>\n" );
document.write( "\n" );
document.write( "When you plot all those points, you'll see that the two graphs intersect at x=0 and x=1.  This verifies our algebraic answer.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C200%2C-1%2C6%2C-1%2C4%2Cx%2Csqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C200%2C-1%2C6%2C-1%2C4%2Cx%2Csqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Happy Calculating!!! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );