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 144 m². 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.
When each side is increased by 7 m, the new length of each side is x + 7, and the new total area is (x + 7)^2 = 144.
Expanding (x + 7)^2, we get x^2 + 14x + 49 = 144.
Rearranging the equation, we get x^2 + 14x + 49 - 144 = 0.
This simplifies to x^2 + 14x - 95 = 0.
Factoring the quadratic equation, we get (x + 19)(x - 5) = 0.
Setting each factor to zero, we get x = -19 and x = 5. Since the length of a side cannot be negative, the length of each side of the original garden is 5 m.