Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is increased by 7 m, the new total area of the garden will be 169 m^2. Find the length of each side of the original garden.
Let's assume the length of one side of the original garden is x. The area of the original garden is x^2 m^2.
If each side of the original garden is increased by 7m, the new length of one side of the expanded garden will be x + 7 m.
The new area of the expanded garden will be (x + 7)^2 m^2 = x^2 + 14x + 49 m^2.
Given that the new total area of the expanded garden is 169 m^2, we can write the equation:
x^2 + 14x + 49 = 169.
To solve this quadratic equation, we bring all terms to one side and simplify:
x^2 + 14x + 49 - 169 = 0,
x^2 + 14x - 120 = 0.
Next, we factorize the quadratic equation:
(x - 6)(x + 20) = 0.
Setting each factor to zero, we have two possible solutions for x:
x - 6 = 0 or x + 20 = 0.
Solving each equation, we have:
x = 6 or x = -20.
Since the length of a side cannot be negative, we disregard the solution x = -20.
Therefore, the length of each side of the original garden is x = 6 meters. Answer: \boxed{6}.