Question

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

See example.
(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 solutions for the quadratic equation \((2x - 7)(x + 9) = 0\), you'll substitute the given values for \(x\) and evaluate whether the equation holds true.

Let’s go through the values given in the table you provided, performing the steps for each value.

### Value 0:
1. **Substitute:** \((2(0) - 7)(0 + 9) = 0\)
2. **Evaluate: Step 1:** \((-7)(9)\)
3. **Step 2:** \(-63 = 0\)
4. **True or False Statement?** False

### Value 3:
1. **Substitute:** \((2(3) - 7)(3 + 9) = 0\)
2. **Evaluate: Step 1:** \((6 - 7)(12)\)
3. **Step 2:** \((-1)(12) = -12\)
4. **True or False Statement?** False

### Value -9:
1. **Substitute:** \((2(-9) - 7)(-9 + 9) = 0\)
2. **Evaluate: Step 1:** \((-18 - 7)(0)\)
3. **Step 2:** \((-25)(0) = 0\)
4. **True or False Statement?** True

### Value 9:
1. **Substitute:** \((2(9) - 7)(9 + 9) = 0\)
2. **Evaluate: Step 1:** \((18 - 7)(18)\)
3. **Step 2:** \((11)(18) = 198\)
4. **True or False Statement?** False

### Summary Table:

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

The roots of the original equation \((2x - 7)(x + 9) = 0\) are found using the Zero Product Property, leading to the solutions \(x = \frac{7}{2}\) and \(x = -9\). Among the substituted values, only \(x = -9\) satisfies the equation.