document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=409413>Question 409413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In solving the equation (x + 2)(x – 2) = 32, Eric stated that the solution would be<BR>\n" );
document.write( "x + 2 = 32 => x = 30<BR>\n" );
document.write( "or<BR>\n" );
document.write( "(x – 2) = 32 => x = 34<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 #288232 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=288232\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is no special product rule for 32. There are an infinite number of products that can equal 32.<br><BR>\n" );
document.write( "But there is a special product rule for 0. If a product is zero, then one (or more) of the factors must be zero. So we need to manipulate the equation so it is a product that equals zero.<br><BR>\n" );
document.write( "First we simplify the left side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4+=+32 ALIGN=MIDDLE  ALT=\"x%5E2-4+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we make one side zero. Subtracting 32 from each side we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-36+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-36+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we factor. This is a difference of squares so it is easy to factor:<BR>\n" );
document.write( "(x+6)(x-6) = 0<BR>\n" );
document.write( "With this product that equals zero we know that one of the factors must be zero. So:<BR>\n" );
document.write( "x+6 = 0 or x-6 = 0<BR>\n" );
document.write( "Solving each of these we get:<BR>\n" );
document.write( "x = -6 or x = 6<BR>\n" );
document.write( "So there are two solutions to the original equation. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );