Final answer:
To find the value of x when the side length of a square is 4x + 3 and the area is 121 square units, you set up and solve the equation (4x + 3)² = 121. The solution is x = 2.
Step-by-step explanation:
If the side length of a square is represented by 4x + 3 and its area is 121 square units, to find the value of x, we can set up the equation:
(4x + 3)2 = 121
By solving the equation:
- Expand the left side: (4x + 3)(4x + 3) = 16x2 + 12x + 12x + 9
- Simplify: 16x2 + 24x + 9 = 121
- Subtract 121 from both sides: 16x2 + 24x - 112 = 0
- Divide all terms by 8: 2x2 + 3x - 14 = 0
- Factor the quadratic: (2x + 7)(x - 2) = 0
- Solve for x: x = -7/2 or x = 2
- Since a side length cannot be negative, the value of x must be 2.