To find the width of the driveway in terms of $x$, we can start by using the given formula for the area of the rectangle, $A = \text{length} \times \text{width}$.

Given:

• Area $A = 5x^2 + 43x - 18$
• Length $\ell = x + 9$

The formula for the width $w$ can be derived from the area formula: $A = \ell \times w$ $5x^2 + 43x - 18 = (x + 9) \times w$

Now, solving for $w$: $w = \frac{5x^2 + 43x - 18}{x + 9}$

Let's simplify this expression to find the width $w$ in terms of $x$.The width of the driveway in terms of $x$ is $5x - 2$.

Would you like more details on how this was derived or have any other questions?

Here are some related questions you might consider:

1. How would the dimensions change if the area formula was different?
2. What happens to the width if the value of $x$ is increased or decreased?
3. How can we verify this solution is correct by plugging in values for $x$?
4. What is the perimeter of the driveway given this width?
5. Could the width be expressed in a different form if the area had different coefficients?

Tip: When dealing with quadratic equations, factoring or using the quadratic formula are effective methods to find roots or simplify expressions involving $x$.