To solve the equation (x - 3)^2 = 49, we can take the square root of both sides to eliminate the exponent of 2. However, when taking the square root, we need to consider both the positive and negative square roots.
(x - 3)^2 = 49
Taking the square root of both sides, we get:
√((x - 3)^2) = ±√49
Simplifying, we get:
x - 3 = ±7
Adding 3 to both sides, we get:
x = 3 ± 7
So the possible values of x are:
x = 3 + 7 = 10
x = 3 - 7 = -4
Therefore, the correct values of x are -4 and 10. The options given are -46, -4, 10, and 52. So the correct values of x from the options are -4 and 10.