Question 366046: 1. In solving the equation (x + 4)(x – 4) = 33, Eric stated that the solution would be
x + 4 = 33 => x = 29
or
(x – 4) = 33 => x = 37
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning
Found 2 solutions by Jk22, CharlesG2:
Answer by Jk22(389)   (Show Source):
You can put this solution on YOUR website! Suppose
x + 4 = 33 => x = 29
then x - 4 = 25, hence (x+4)(x-4) were bigger than 33
(X+4)(x-4) is a product,we shall here write 33 as a product, we find : 33 = 3 * 11 (primary decomposition)
moreover we notice that 11 = 3 + 8 = 3 + 2*4, which is the difference between x+4 and x-4, and this should be the solution.
hence we take x = 3 + 4 = 7 the middle point : we have x - 4 = 3, x + 4 = 11
thus (x+4)(x-4)=11 * 3 = 33
THe other way is expanding : (X+4)(X-4) = x^2 - 16 = 33
hence x^2 = 49, solutions are +7 and -7.
Answer by CharlesG2(834)  (Show Source):
You can put this solution on YOUR website! "1. In solving the equation (x + 4)(x – 4) = 33, Eric stated that the solution would be
x + 4 = 33 => x = 29
or
(x – 4) = 33 => x = 37
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning"
because Eric is doing it wrong that is why his solutions are failing
(x + 4)(x - 4) = 33
using FOIL, First Outer Inner Last
x^2 - 4x + 4x - 16 = 33
x^2 - 16 = 33 (the 4x's canceled out)
x^2 = 33 + 16 (brought 16 over to the right side)
x^2 = 49
x = +- 7 (these are the values of x that work, 7 and -7)
check 7 and -7:
(7 + 4)(7 - 4) = 11 * 3 = 33, yes
(-7 + 4)(-7 - 4) = -3 * -11 = 33, yes
(x + 4)(x – 4) = 33
trying x = 29
(29 + 4)(29 - 4) = 33 * 25 = 825, this no were near 33
tring x = 37
(37 + 4)(37 - 4) = 41 * 33 = 1353, this way more than 33
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