document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72601>Question 72601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am kind of stuck on this problem... maybe someone can assist me! any help would be greatly appreciated!\r<BR>\n" );
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document.write( " 	For the equation x - &#8730;x = 0, perform the following:<BR>\n" );
document.write( "a) 	Solve for all values of x that satisfies the equation.<BR>\n" );
document.write( "Answer: \r<BR>\n" );
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document.write( "Show work in this space	\r<BR>\n" );
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document.write( "b) 	Graph the functions y = x  and y = &#8730;x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.\r<BR>\n" );
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document.write( "Graph \r<BR>\n" );
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document.write( "c) 	How does the graph relate to part a?<BR>\n" );
document.write( "Answer: 	<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 #51903 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=51903\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First Problem:<BR>\n" );
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document.write( "Solve the equation <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;\" > for all values of x that will satisfy the equation:<BR>\n" );
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document.write( "First 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 of the equation.  When you do, the equation becomes:<BR>\n" );
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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;\" ><BR>\n" );
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document.write( "Next square both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+%28sqrt%28x%29%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+=+%28sqrt%28x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes <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" );
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document.write( "Then subtract x from both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the left side factor an x:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2A%28x-1%29+=+0 ALIGN=MIDDLE  ALT=\"x%2A%28x-1%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that this equation will be true if either of the factors on the left side equals zero.<BR>\n" );
document.write( "This is true because if one of the factors on the left side is zero, the entire left<BR>\n" );
document.write( "side will be zero and therefore will equal the right side. So set each of the two factors<BR>\n" );
document.write( "equal to zero and you get:<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;\" > and<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1+=0 ALIGN=MIDDLE  ALT=\"x-1+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and by adding 1 to both sides of this equation you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "So there are two answers to this equation: <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If you substitute<BR>\n" );
document.write( "0 for x and if you next substitute 1 for x in the original equation you will see that these<BR>\n" );
document.write( "two answers work. <BR>\n" );
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document.write( "Next graph y = x and y = sqrt(x) on the same set of axes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C+800%2C-3%2C6%2C-3%2C6%2Cx%2C+sqrt%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C+800%2C-3%2C6%2C-3%2C6%2Cx%2C+sqrt%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The green graph represents the y = square root of x and the red graph represents y = x. Note<BR>\n" );
document.write( "that the green graph should hit the origin, but there is a flaw in the drafting program that<BR>\n" );
document.write( "does not do that.  So you will have to make your version of the green graph go down to the<BR>\n" );
document.write( "origin.<BR>\n" );
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document.write( "What is the connection where the graphs cross.  The crossing points occur at x = 0 and x = 1<BR>\n" );
document.write( "which are the answers we got for the problem.  At those two points x and the square root of<BR>\n" );
document.write( "x are equal so that when you subtract them, the answer is zero.  <BR>\n" );
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document.write( "Hope this helps you to understand the problem. </SPAN>\n" );
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