(x-16)^2=64

multiply x - 16 by itself

(x-16)(x-16)

x^2 -32x + 256 = 64

subtract 64 from both side

x^2 - 32x +192=0

factor or use quadratic formula

its factor is (x -8 and x-24) set equal to zero and solve for x

To solve the equation (x-16)^2 = 64, we can follow these steps:

Step 1: Expand the squared term (x-16)^2 using the foil method.
(x-16)*(x-16) = 64

Step 2: Simplify the equation.
x^2 - 2*16*x + 16^2 = 64
x^2 - 32*x + 256 = 64

Step 3: Subtract 64 from both sides of the equation.
x^2 - 32*x + 192 = 0

Step 4: Solve the quadratic equation.
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, let's use factoring.

The equation can be factored as:
(x - 16)(x - 12) = 0

Setting each factor equal to zero, we have two possible solutions:
x - 16 = 0 or x - 12 = 0

Solving for x in each equation:
x = 16 or x = 12

Therefore, the solutions for the given equation are x = 16 and x = 12.