Question

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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 solve the table using the quadratic equation \((2x−7)(x+9) = 0\), we need to substitute the given values of \(x\) into the equation and evaluate.

Let's fill in the table step by step for each provided value.

**1. Value = 0**
- Substitute \(x = 0\):
\((2(0)−7)((0+9)) = (−7)(9)\)
- Evaluate:
- Step 1: \((−7)(9) = −63\)
- Step 2: Statement: \(-63 = 0\) (False)

**2. Value = -9**
- Substitute \(x = -9\):
\((2(-9)−7)((-9+9)) = (−18−7)(0)\)
- Evaluate:
- Step 1: \((-25)(0) = 0\)
- Step 2: Statement: \(0 = 0\) (True)

**3. Value = 3**
- Substitute \(x = 3\):
\((2(3)−7)((3+9)) = (6−7)(12)\)
- Evaluate:
- Step 1: \((-1)(12) = -12\)
- Step 2: Statement: \(-12 = 0\) (False)

**4. Value = 9**
- Substitute \(x = 9\):
\((2(9)−7)((9+9)) = (18−7)(18)\)
- Evaluate:
- Step 1: \((11)(18) = 198\)
- Step 2: Statement: \(198 = 0\) (False)

Now, let's summarize our findings in the table format:

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

This table should help you check and organize your evaluation! If you have any further questions, feel free to ask.