In solving the equation (x + 3)(x – 3) = -8, Eric stated that the solution would be
x + 3 = -8 = x = -11
or
(x – 3) = -8 = x = -5
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.

Question

In solving the equation (x + 3)(x – 3) = -8, Eric stated that the solution would be
x + 3 = -8 => x = -11
or
(x – 3) = -8 => x = -5
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.

anonymous · Answer

x = 1 because if the two binomials are multiplied, you get:
$$x^{2}-9 = -8$$
$$x^{2} = -8+9$$
$$\sqrt{x}$$ or x = 1 or -1