Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 5 m, the new total area of the garden will be 196 m^2. Find the length of each side of the original garden.
Let the length of each side of the original square garden be x m.
The area of the original garden is x^2 m^2.
The new length of each side of the expanded garden is x + 5 m.
The area of the expanded garden is (x + 5)^2 = 196 m^2.
Expanding the square, we have x^2 + 10x + 25 = 196.
Subtracting 196 from both sides, we get x^2 + 10x - 171 = 0.
Factoring the quadratic equation, we have (x + 19)(x - 9) = 0.
Setting each factor equal to zero, we have two solutions: x + 19 = 0 or x - 9 = 0.
Solving for x in each equation gives us x = -19 or x = 9.
Since the length of a side cannot be negative, the length of each side of the original garden is 9 m. Answer: \boxed{9}.