1. **State the problem:** We have a rectangular garden PQRS with sides QR = 80 m and SR = (5x + 8) m. The garden has grassy areas WSV and TQU, and the rest is a cemented area PTURVW with area 9600 m^2. We need to form a quadratic equation for $x$ based on this information. 2. **Formula for area of rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ Here, total area of PQRS is: $$80 \times (5x + 8) = 400x + 640$$ 3. **Areas of grassy triangles:** - Triangle WSV has area: $$\frac{1}{2} x^2$$ - Triangle TQU has area: $$\frac{1}{2} \times 2x \times 2x = 2x^2$$ 4. **Area of cemented region:** The cemented area is total area minus grassy areas: $$\text{Cemented area} = (400x + 640) - \left( \frac{1}{2} x^2 + 2x^2 \right) = 9600$$ 5. **Simplify the equation:** Combine grassy areas: $$\frac{1}{2} x^2 + 2x^2 = 2.5x^2$$ So, $$400x + 640 - 2.5x^2 = 9600$$ 6. **Rearrange to standard quadratic form:** $$-2.5x^2 + 400x + 640 - 9600 = 0$$ $$-2.5x^2 + 400x - 8960 = 0$$ This is the quadratic equation formed based on the problem. **Final answer:** $$-2.5x^2 + 400x - 8960 = 0$$