<PRE><B>Question 30224</B>
x^2+8x+7=0   ----(1)
x^2+(7x+x)+7=0  (splitting the middle term into two parts whose sum is 8x and their product is the product of the square term and the constant term) 
(x^2+7x)+(x+7)=0  (additive associativity)
x(x+7)+1(x+7) = 0
xp+ p = 0 where p = (x+7)
p(x+1) = 0 
(x+7)(x+1) = 0
(x+7) =0 gives  x = -7
(x+1) =0 gives  x = -1
Answer: x = -1 and x = -7
Verification: x=-1 in (1) gives 
LHS = x^2+8x+7 = 1-8+7 = 0 = RHS
x=-7 in (1) gives 
LHS = x^2+8x+7 = 49-56+7 = 0 = RHS
Hence our values are correct

The second problem should be
x^2+12x+11=0

Similar to the above
x^2+12x+11=0
(x+11)(x+1) = 0 (sum is 12 and the product is 11 and so the quantities are 
11 and 1)
(x+11) =0 gives  x = -11
(x+1) =0 gives  x = -1
Answer: x = -1 and x = -11
Verification: x=-1 in (1) gives 
LHS = x^2+12x+11 = 1-12+11 = 0 = RHS
x=-11 in (1) gives 
LHS = x^2+12x+11 = 121-132+11 = 0 = RHS
Hence our values are correct







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