document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446534>Question 446534</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the product of a number and 4 less than the number is 32. find the numbers </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307522 by </B><A HREF=/tutors/aboutme.mpl?userid=duckness73><B>duckness73(47)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=duckness73><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=duckness73><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=307522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = the first number; which means that x - 4 is the second number.  Since we know the product of the two numbers is 32, that means that if you multiply them together, you get 32.  Here's the equation:\r<BR>\n" );
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document.write( "x (x - 4) = 32\r<BR>\n" );
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document.write( "Let's expand the left side:\r<BR>\n" );
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document.write( "And, solving for x we have:<BR>\n" );
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document.write( "Then, factoring, we have:\r<BR>\n" );
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document.write( "(x-8)(x+4) = 0<BR>\n" );
document.write( "x = 8 or x = -4\r<BR>\n" );
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document.write( "In the first case, where x = 8, that would mean that x - 4 = 8 - 4 = 4.  And, 8 times 4 is 32.  So the pair of 8 and 4 works.\r<BR>\n" );
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document.write( "In the second case, where x = -4, that would mean that x - 4 = -4 - 4 = -8.  And, -4 times -8 is again 32.  So the pair -4 and -8 works.<BR>\n" );
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