Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7m, the new total area of the garden will be 169m^2. Find the length of each side of the original garden.
Let x be the length of each side of the original garden.
The area of the original garden is x^2.
The area of the expanded garden is (x+7)^2 = 169.
Expanding the equation gives x^2 + 14x + 49 = 169.
Subtracting 169 from both sides gives x^2 + 14x - 120 = 0.
Factoring the left side gives (x + 20)(x - 6) = 0.
Setting each factor to 0 gives x = -20 or x = 6.
Since the length of a side cannot be negative, the length of each side of the original garden is 6 meters. Answer: \boxed{6}.