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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.