Problema Solution
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
Answer provided by our tutors
The solution Eric applied is valid only when equated to zero as it is using zero property of equality. So the correct solution to this problem is to expand and equate one side of the equation to 0. We have:
(x+4)(x-4) = 33
x2-16 = 33
x2-16-33 = 0
x2-49 = 0
(x+7)(x-7) = 0
x+7 = 0
x = -7
x-7 = 0
x = 7
So the correct answers are:
x = -7 and x = 7