Expanding both sides of the equation, we get:
(x - 6)(x - 6) = (7 - x)(7 - x)x^2 - 6x - 6x + 36 = 49 - 7x - 7x + x^2x^2 - 12x + 36 = 49 - 14x + x^212x - 14x = 49 - 36-2x = 13x = -6.5
Therefore, the solution to the equation (x - 6)^2 = (7 - x)^2 is x = -6.5.
Expanding both sides of the equation, we get:
(x - 6)(x - 6) = (7 - x)(7 - x)
x^2 - 6x - 6x + 36 = 49 - 7x - 7x + x^2
x^2 - 12x + 36 = 49 - 14x + x^2
12x - 14x = 49 - 36
-2x = 13
x = -6.5
Therefore, the solution to the equation (x - 6)^2 = (7 - x)^2 is x = -6.5.