Solve: \( (x-4)^{2}+4=49 \) \( x=-4 \pm 2 \sqrt{10} \) \( x=-4+\sqrt{45} \) \( x= \pm 7 \) \( x=4 \pm 3 \sqrt{5} \)

To solve the equation \( (x-4)^{2}+4=49 \), we start by isolating the squared term. First, we subtract 4 from both sides: \[ (x-4)^{2} = 45 \] Next, we take the square root of both sides: \[ x - 4 = \pm \sqrt{45} \] Now, we can simplify \(\sqrt{45}\): \[ \sqrt{45} = 3 \sqrt{5} \] Thus, we can express the equation as: \[ x - 4 = \pm 3 \sqrt{5} \] Finally, we add 4 to both sides to solve for \(x\): \[ x = 4 \pm 3 \sqrt{5} \] So the correct solution is: \( x = 4 \pm 3 \sqrt{5} \) The other options do not satisfy the original equation when evaluated. Always check your work for extraneous solutions!