document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=494576>Question 494576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I really need help please.\r<BR>\n" );
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document.write( "In solving the equation (x + 1)(x – 2) = 54, Eric stated that the solution would be<BR>\n" );
document.write( "x + 1 = 54 => x = 53<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(x – 2) = 54 => x = 56<BR>\n" );
document.write( "However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #335703 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=335703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In solving the equation (x + 1)(x – 2) = 54, Eric stated that the solution would be<BR>\n" );
document.write( "x + 1 = 54 => x = 53<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(x – 2) = 54 => x = 56<BR>\n" );
document.write( "However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.<BR>\n" );
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document.write( "Eric's reasoning is only valid if the RHS of the equation is equal to 0.  <BR>\n" );
document.write( "Then if either of the two factors are equal to 0, this makes the whole<BR>\n" );
document.write( "expression equal to 0.  If the RHS is not equal to 0, then the two factors when<BR>\n" );
document.write( "multiplied together have to equal the RHS, not each of the factors individually.<BR>\n" );
document.write( "To solve, first multiply the two factors and then subtract the RHS:<BR>\n" );
document.write( "(x+1)(x-2) = 54<BR>\n" );
document.write( "x^2 - x - 2 = 54<BR>\n" );
document.write( "x^2 - x - 56 = 0<BR>\n" );
document.write( "The above equation can be factored as:<BR>\n" );
document.write( "(x-8)(x+7) = 0<BR>\n" );
document.write( "We see from this that the solutions are x = 8 and x = -7 </SPAN>\n" );
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