document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134826>Question 1134826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangle has a length of 12 meters less than 2 times its width.  If the area of the rectangle is 2574<BR>\n" );
document.write( "square meters, find the length of the rectangle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---- meters? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #752309 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=752309\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area = L x W = 2574<BR>\n" );
document.write( "L = 2W-12 substitute for L above:<BR>\n" );
document.write( "2W-12 x W = 2574<BR>\n" );
document.write( "2W^2-12W = 2574<BR>\n" );
document.write( "2W^2-12W-5148 = 0<BR>\n" );
document.write( "2(W^2-6W-2574) = 0<BR>\n" );
document.write( "The easiest way would be by factoring. To do this, we multiply the coefficient of the 1st element times the constant: 1 x -2574 = -2574<BR>\n" );
document.write( "Break down -2574 into its factors to see if we get to two factorswhose sum equals the coefficient of the middle term, which is -6:<BR>\n" );
document.write( "-2574+1 =    	-2573 	<BR>\n" );
document.write( "-1287+2 =    	-1285 	<BR>\n" );
document.write( "-858+3 =    	-855 	<BR>\n" );
document.write( "-429+6 =    	-423 	<BR>\n" );
document.write( "-286+9 =    	-277 	<BR>\n" );
document.write( "-234+11 =    	-223<BR>\n" );
document.write( "etc. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you continue, you will discover that there aren't two factors that would add to -6, so this trinomial cannot be factored.<BR>\n" );
document.write( "Without wasting any more time, I will solve by completing the squares, a method which can solve all quadratic equations:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "2W^2-12W = 2574 divide both sides by 2:<BR>\n" );
document.write( "w^2-6W = 1287 <BR>\n" );
document.write( "now write the equation in the form x^2+2ax+a^2 = (x+a)^2:<BR>\n" );
document.write( "2aW = -6W; 2a = -6; a = -3<BR>\n" );
document.write( "add a^2 to both sides:<BR>\n" );
document.write( "a^2 = -3^2 = 9<BR>\n" );
document.write( "W^2-6W+(-3)^2 = 1287+(-3)^2<BR>\n" );
document.write( "W^2+(-3)^2 = 1296<BR>\n" );
document.write( "Complete the squares:<BR>\n" );
document.write( "(W-3)^2 = 1296<BR>\n" );
document.write( "W-3 = sqrt(1296)<BR>\n" );
document.write( "W-3 = sqrt(36^2)<BR>\n" );
document.write( "W-3 = 36<BR>\n" );
document.write( "W = 39<BR>\n" );
document.write( ".<BR>\n" );
document.write( "W-3 = -sqrt(1296)<BR>\n" );
document.write( "W-3 = -36<BR>\n" );
document.write( "W = -33<BR>\n" );
document.write( ".<BR>\n" );
document.write( "I tried 39 in our equation 2W-12 x W = 2574 and it doesn't work. Let's try -33:<BR>\n" );
document.write( "2W^2-12W = 2574<BR>\n" );
document.write( "2(-33)^2-12(-33) = 2574<BR>\n" );
document.write( "2(1089)+396 = 2574<BR>\n" );
document.write( "2178+396 = 2574 Correct<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Happy learning </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );