Final answer:
To find the value of x, the equation (2x + 3)² = 121 is solved to get x = 4, which is the correct value for x as the side length of the square expressed by the equation can not be negative.
Step-by-step explanation:
To find the value of x for a square with a side length expressed as 2x + 3 and an area of 121 square meters, we first write the equation for the area of a square, which is side length squared (A = s²). Plugging in the given expression for the side length, we have:
(2x + 3)² = 121
Expanding the left side, we get:
4x² + 12x + 9 = 121
To solve for x, we set the equation equal to zero:
4x² + 12x + 9 - 121 = 0
4x² + 12x - 112 = 0
We can simplify this quadratic equation by dividing all terms by 4:
x² + 3x - 28 = 0
Factoring the quadratic, we find:
(x + 7)(x - 4) = 0
Therefore, x could be -7 or 4. Since a side length of a square cannot be negative, we discard -7 and conclude that:
x = 4
When x is 4, the side length of the square is:
2(4) + 3 = 11 meters.
The side length matches the square root of the area given, thus confirming our solution is correct.