Answer: x = 1 and x = 13.
Step-by-step explanation: To solve the equation (x - 7)^2 = 36, we can first rewrite the equation as x^2 - 14x + 49 = 36.
Next, we can rewrite the equation as x^2 - 14x + 13 = 0.
To solve for x, we can then use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
where a = 1, b = -14, and c = 13.
Substituting these values into the formula, we get:
x = (14 +/- sqrt(14^2 - 4(1)(13))) / 2
x = (14 +/- sqrt(196 - 52)) / 2
x = (14 +/- sqrt(144)) / 2
x = (14 +/- 12) / 2
The values of x are therefore 1 and 13.
Therefore, the correct answer is x = 1 and x = 13.