Final answer:
The correct solutions to the quadratic equation 4(x+4)^2 = 36 are x = -1 and x = -7, which are not listed among the provided options.
Step-by-step explanation:
To solve the quadratic in vertex form 4(x+4)^2 = 36, we first need to isolate the squared term by dividing both sides of the equation by 4, which gives us (x+4)^2 = 9. Next, we can take the square root of both sides to obtain x+4 = ±3. This means we have two possible solutions for x, which are x = -4 + 3 or x = -4 - 3. Simplifying these, we get x = -1 and x = -7. None of the options provided (a. x = 3, b. x = -3, c. x = 4, d. x = -4) match the correct solutions.