document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=572911>Question 572911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When 36 is subtracted from the square of a number, the result is 5 times the number. Find the negative solution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #368565 by </B><A HREF=/tutors/aboutme.mpl?userid=mathsmiles><B>mathsmiles(68)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathsmiles><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=mathsmiles><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=368565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X = a number we're looking for.\r<BR>\n" );
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document.write( "If we subtract 36 from the square of that number, X^2 - 36 ... <BR>\n" );
document.write( "The result is equal to 5 times the number, 5X<BR>\n" );
document.write( "Therefore, <BR>\n" );
document.write( "X^2 - 36 = 5X\r<BR>\n" );
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document.write( "You've probably seen this solved by putting the equation in the form:<BR>\n" );
document.write( "aX^2 - bX - c = 0\r<BR>\n" );
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document.write( "Doing that here, we subtract 5X from both sides to make the right side of the equation equal to zero.\r<BR>\n" );
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document.write( "X^2 - 5X - 36 = 0<BR>\n" );
document.write( "Now we need to factor this.\r<BR>\n" );
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document.write( "(X _  _   )(X _  _  ) = 0 (where _ denotes an operator or term that we need.)<BR>\n" );
document.write( "Looking at the operators, we see that the operands are different, so<BR>\n" );
document.write( "(X - _  )(X +  _  ) = 0   (we have operator, need term.)<BR>\n" );
document.write( "Now we need to find two factors of 36 whose difference is 5.  So let's try a few:<BR>\n" );
document.write( "36 = 6 X 6  Nope<BR>\n" );
document.write( "36 = 12 X 3 Nope<BR>\n" );
document.write( "36 = 9 X 4  Yup!\r<BR>\n" );
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document.write( "Since the middle term is negative, we know the placement of the 9 and 4.<BR>\n" );
document.write( "(X-9)(X+4)= 0<BR>\n" );
document.write( "Therefore, X-9=0   or X+4=0<BR>\n" );
document.write( "X-9=0  => X=9<BR>\n" );
document.write( "X+4=0  => X=-4\r<BR>\n" );
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document.write( "Going back to the original problem, it says \"Find the negative solution.\" <BR>\n" );
document.write( "Therefore, X=-4.\r<BR>\n" );
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document.write( "Let's check:<BR>\n" );
document.write( "(-4)^2-36 = 5*(-4)<BR>\n" );
document.write( "16-36 = -20<BR>\n" );
document.write( "-20=-20  Check!<BR>\n" );
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