To solve the quadratic equation \((2x - 7)(x + 9) = 0\) by substitution, we need to substitute the given values into the equation and evaluate whether the result is zero.
We will check the values \(0\), \(3\), \(-9\), and \(9\).
1. For \( x = 0 \):
Substitution: \[ (2(0) - 7)(0 + 9) = (0 - 7)(9) = (-7)(9) = -63 \] This means: \[ -63 \neq 0 \quad \text{(False)} \]
2. For \( x = 3 \):
Substitution: \[ (2(3) - 7)(3 + 9) = (6 - 7)(12) = (-1)(12) = -12 \] This means: \[ -12 \neq 0 \quad \text{(False)} \]
3. For \( x = -9 \):
Substitution: \[ (2(-9) - 7)(-9 + 9) = (-18 - 7)(0) = (-25)(0) = 0 \] This means: \[ 0 = 0 \quad \text{(True)} \]
4. For \( x = 9 \):
Substitution: \[ (2(9) - 7)(9 + 9) = (18 - 7)(18) = (11)(18) = 198 \] This means: \[ 198 \neq 0 \quad \text{(False)} \]
Summary of Results:
- For \( x = 0 \): False
- For \( x = 3 \): False
- For \( x = -9 \): True
- For \( x = 9 \): False
You can now fill in the table with the results. If you need further assistance, let me know!