SOLUTION: In solving the equation (x + 2)(x � 2) = 32, Eric stated that the solution would be x + 2 = 32 => x = 30 or (x � 2) = 32 => x = 34 However, at least one of these solutions fail

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 409413: In solving the equation (x + 2)(x � 2) = 32, Eric stated that the solution would be
x + 2 = 32 => x = 30
or
(x � 2) = 32 => x = 34
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.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
There is no special product rule for 32. There are an infinite number of products that can equal 32.

But there is a special product rule for 0. If a product is zero, then one (or more) of the factors must be zero. So we need to manipulate the equation so it is a product that equals zero.

First we simplify the left side:

Next we make one side zero. Subtracting 32 from each side we get:

Now we factor. This is a difference of squares so it is easy to factor:
(x+6)(x-6) = 0
With this product that equals zero we know that one of the factors must be zero. So:
x+6 = 0 or x-6 = 0
Solving each of these we get:
x = -6 or x = 6
So there are two solutions to the original equation.