To solve the equations:

1) (x-3)^2=25
Expand the left side:
(x-3)(x-3) = 25
x^2 - 3x - 3x + 9 = 25
x^2 - 6x + 9 = 25
x^2 - 6x - 16 = 0
Now we have a quadratic equation, so we can solve for x using the quadratic formula:
x = [6 +/- sqrt((-6)^2 - 41(-16))] / 2(1)
x = [6 +/- sqrt(36 + 64)] / 2
x = [6 +/- sqrt(100)] / 2
x = [6 +/- 10] / 2

Therefore, x can be either x = 8 or x = -2.

2) (x+4)^2 = 9
Expand the left side:
(x+4)(x+4) = 9
x^2 + 4x + 4x + 16 = 9
x^2 + 8x + 16 = 9
x^2 + 8x + 16 - 9 = 0
x^2 + 8x + 7 = 0
Now we have another quadratic equation, so we can solve for x using the quadratic formula:
x = [-8 +/- sqrt(8^2 - 417)] / 2(1)
x = [-8 +/- sqrt(64 - 28)] / 2
x = [-8 +/- sqrt(36)] / 2
x = [-8 +/- 6] / 2

Therefore, x can be x = -7 or x = -1.