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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


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Answer 1

Let's evaluate the quadratic equation \((2x−7)(x+9) = 0\) by substituting the given values into the equation and checking whether or not they satisfy the equation.

### Evaluating Given Values

#### For Value 0:
1. **Substitute:** \(x = 0\)
\[
(2(0)−7)(0+9) = (−7)(9) = -63
\]
2. **Evaluate:**
- The equation equals \(-63\), which does not equal \(0\).
3. **True or False Statement:** \(-63 = 0\) **False**

#### For Value 3:
1. **Substitute:** \(x = 3\)
\[
(2(3)−7)(3+9) = (6−7)(12) = (−1)(12) = -12
\]
2. **Evaluate:**
- The equation equals \(-12\), which does not equal \(0\).
3. **True or False Statement:** \(-12 = 0\) **False**

#### For Value -9:
1. **Substitute:** \(x = -9\)
\[
(2(-9)−7)(-9+9) = (−18−7)(0) = (−25)(0) = 0
\]
2. **Evaluate:**
- The equation equals \(0\), which does equal \(0\).
3. **True or False Statement:** \(0 = 0\) **True**

#### For Value 9:
1. **Substitute:** \(x = 9\)
\[
(2(9)−7)(9+9) = (18−7)(18) = (11)(18) = 198
\]
2. **Evaluate:**
- The equation equals \(198\), which does not equal \(0\).
3. **True or False Statement:** \(198 = 0\) **False**

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

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