document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=395137>Question 395137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain the error made in solving the equation.  Solve the equation correctly<BR>\n" );
document.write( "x^2=x<BR>\n" );
document.write( "x^2/x=x/x<BR>\n" );
document.write( "x=1\r<BR>\n" );
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document.write( "I thought the error was that x^2 is not equal to x, but rather x^2 is equal to x*x and so it should have been multiplication and not division-yet I really don't know I am only taking a guess.  I also don't know how to go about solving the equation itself </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #280447 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=280447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The process is correct. However you're assuming that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C%3E+0 ALIGN=MIDDLE  ALT=\"x+%3C%3E+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since you're dividing by x (this part is the mistake) which is assumed to be non-zero so that the operation is defined. If x = 0, the equation is still true, so x = 0 or x = 1.\r<BR>\n" );
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document.write( "The best way to solve this is to move x to the other side to produce\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "x = 0, 1\r<BR>\n" );
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document.write( "Or, you could do it like the way you did in the question (assuming <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E0 ALIGN=MIDDLE  ALT=\"x%3C%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), then do the <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;\" > case and see if it works. However the first method is more solid. </SPAN>\n" );
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