Expanding each side of the equation:
(x+2)^2 = (x+2)(x+2) = x^2 + 4x + 4
(x-4)^2 = (x-4)(x-4) = x^2 - 8x + 16
So the original equation simplifies to:
x^2 + 4x + 4 = x^2 - 8x + 16
Now we can combine like terms and simplify:
4x + 4 = -8x + 16
Adding 8x to both sides:
12x + 4 = 16
Subtracting 4 from both sides:
12x = 12
Dividing by 12 on both sides:
x = 1
Therefore, the solution to the equation is x = 1.
Expanding each side of the equation:
(x+2)^2 = (x+2)(x+2) = x^2 + 4x + 4
(x-4)^2 = (x-4)(x-4) = x^2 - 8x + 16
So the original equation simplifies to:
x^2 + 4x + 4 = x^2 - 8x + 16
Now we can combine like terms and simplify:
4x + 4 = -8x + 16
Adding 8x to both sides:
12x + 4 = 16
Subtracting 4 from both sides:
12x = 12
Dividing by 12 on both sides:
x = 1
Therefore, the solution to the equation is x = 1.