Question

Given the quadratic equation (2x−7)(x+9)
check the solution in the following table by substitution and evaluating

(1 point)
Value Substituted Evaluate: Step 1 Step 2: True or False Statement?
(2x−7)(x+9)=0
original question
0 (2(0)−7)((0+9)=0
(−7)(9)=0
−63=0
false
3
-9
9

Answer 1

To check the solution of the quadratic equation \((2x - 7)(x + 9) = 0\) by substitution and evaluation, we substitute the given values into the equation. Let’s go through each one provided in the table:

### Step 1: Substitute and Evaluate

1. **Value: 0**
- Substituted: \((2(0) - 7)(0 + 9) = (−7)(9)\)
- Evaluate: Step 1 gives \(-63\)
- Step 2: Is \(-63 = 0\)?
- **Statement: False**

2. **Value: -9**
- Substituted: \((2(-9) - 7)(-9 + 9) = (-18 - 7)(0)\)
- Evaluate: Step 1 gives \((-25)(0)\)
- Step 2: Is \(0 = 0\)?
- **Statement: True**

3. **Value: 3**
- Substituted: \((2(3) - 7)(3 + 9) = (6 - 7)(12)\)
- Evaluate: Step 1 gives \((-1)(12)\)
- Step 2: Is \(-12 = 0\)?
- **Statement: False**

4. **Value: 9**
- Substituted: \((2(9) - 7)(9 + 9) = (18 - 7)(18)\)
- Evaluate: Step 1 gives \((11)(18)\)
- Step 2: Is \(198 = 0\)?
- **Statement: False**

### Conclusion
- **For x = 0:** False
- **For x = -9:** True
- **For x = 3:** False
- **For x = 9:** False

So, the complete table would look like this:

| Value | Substituted | Evaluate: Step 1 | Step 2 | True or False Statement? |
|-------|----------------------------------|-------------------|-----------------------|---------------------------|
| 0 | (2(0)−7)(0+9) = (−7)(9) | -63 | -63 = 0 | False |
| -9 | (2(-9)−7)(-9+9) = (-25)(0) | 0 | 0 = 0 | True |
| 3 | (2(3)−7)(3+9) = (-1)(12) | -12 | -12 = 0 | False |
| 9 | (2(9)−7)(9+9) = (11)(18) | 198 | 198 = 0 | False |