We know the area of a square is given by the formula:

$\text{Area} = \text{side length}^2$

In this case, the side length of the square is expressed as $2x + 3$, and the area is 121 square meters. So, we can set up the equation:

$(2x + 3)^2 = 121$

Now, solve for $x$:

Step 1: Take the square root of both sides

$2x + 3 = \pm \sqrt{121}$

$2x + 3 = \pm 11$

Step 2: Solve for $x$ for both cases

Case 1: $2x + 3 = 11$

$2x = 11 - 3$ $2x = 8$ $x = \frac{8}{2} = 4$

Case 2: $2x + 3 = -11$

$2x = -11 - 3$ $2x = -14$ $x = \frac{-14}{2} = -7$

So, the two possible values of $x$ are $x = 4$ and $x = -7$.

However, since a side length cannot be negative, we reject $x = -7$. Thus, the value of $x$ is:

$x = 4$

Would you like more details or have any further questions?

Here are 5 questions for further exploration:

1. How would the problem change if the area of the square was different, say 225 square meters?
2. What happens if the expression for the side length includes a negative term, such as $-2x + 3$?
3. Can you solve the equation if the side length is given in terms of a more complex polynomial, e.g., $3x^2 + 2x + 1$?
4. What if the figure is not a square but a rectangle with the same expression for length?
5. How do you find the perimeter of the square once you know the value of $x$?

Tip: Always check if the solution makes sense in the context of the problem, such as rejecting negative side lengths for a square!