Question 1134826
Area = L x W = 2574
L = 2W-12 substitute for L above:
2W-12 x W = 2574
2W^2-12W = 2574
2W^2-12W-5148 = 0
2(W^2-6W-2574) = 0
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
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:
-2574+1 =    	-2573 	
-1287+2 =    	-1285 	
-858+3 =    	-855 	
-429+6 =    	-423 	
-286+9 =    	-277 	
-234+11 =    	-223
etc. 
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If you continue, you will discover that there aren't two factors that would add to -6, so this trinomial cannot be factored.
Without wasting any more time, I will solve by completing the squares, a method which can solve all quadratic equations:
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2W^2-12W = 2574 divide both sides by 2:
w^2-6W = 1287 
now write the equation in the form x^2+2ax+a^2 = (x+a)^2:
2aW = -6W; 2a = -6; a = -3
add a^2 to both sides:
a^2 = -3^2 = 9
W^2-6W+(-3)^2 = 1287+(-3)^2
W^2+(-3)^2 = 1296
Complete the squares:
(W-3)^2 = 1296
W-3 = sqrt(1296)
W-3 = sqrt(36^2)
W-3 = 36
W = 39
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W-3 = -sqrt(1296)
W-3 = -36
W = -33
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I tried 39 in our equation 2W-12 x W = 2574 and it doesn't work. Let's try -33:
2W^2-12W = 2574
2(-33)^2-12(-33) = 2574
2(1089)+396 = 2574
2178+396 = 2574 Correct
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Happy learning