To find an equation that has exactly the same solutions as \((x-7)(x+9) = 0\), we first need to identify the solutions to the original equation.
The equation \((x-7)(x+9) = 0\) is satisfied when either factor is equal to zero:
- \(x - 7 = 0 \quad \Rightarrow \quad x = 7\)
- \(x + 9 = 0 \quad \Rightarrow \quad x = -9\)
Thus, the solutions to the equation are \(x = 7\) and \(x = -9\).
To create an equation with the same solutions, we can multiply the factors by any non-zero constant or add or subtract equal terms from both sides, among other operations.
For example, we can write:
- \((x-7)(x+9) = 0\) directly.
- \((x-7)(x+9) - k = 0\) for any \( k \).
- \((x - 7)(x + 9) = c\) for any non-zero constant \(c\).
Any of these forms will also have the solutions \(x = 7\) and \(x = -9\).
If you need options to evaluate, feel free to provide them, and I can help determine which one matches!