1. **State the problem:** We are given the equation for the area of a rectangular garden as $$x(x - 4) = 140$$ where $x$ is the length in feet, and the width is 4 feet less than the length. We need to find the length $x$. 2. **Write the formula:** The area $A$ of a rectangle is given by $$A = \text{length} \times \text{width}$$. 3. **Set up the equation:** Here, $$\text{width} = x - 4$$, so the area equation is $$x(x - 4) = 140$$. 4. **Expand the equation:** $$x^2 - 4x = 140$$ 5. **Bring all terms to one side to form a quadratic equation:** $$x^2 - 4x - 140 = 0$$ 6. **Solve the quadratic equation using the quadratic formula:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-4$, and $c=-140$. 7. **Calculate the discriminant:** $$b^2 - 4ac = (-4)^2 - 4(1)(-140) = 16 + 560 = 576$$ 8. **Calculate the square root of the discriminant:** $$\sqrt{576} = 24$$ 9. **Find the two possible solutions:** $$x = \frac{-(-4) \pm 24}{2(1)} = \frac{4 \pm 24}{2}$$ 10. **Calculate each solution:** - $$x = \frac{4 + 24}{2} = \frac{28}{2} = 14$$ - $$x = \frac{4 - 24}{2} = \frac{-20}{2} = -10$$ 11. **Interpret the solutions:** Length cannot be negative, so discard $x = -10$. 12. **Final answer:** The length of the garden is $$\boxed{14}$$ feet.