Given the quadratic equation (2x−7)(x+9)

Question

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 evaluating for the given values, we'll follow the steps below for each value in the table.

Checking each value

1. When \(x = 0\):

   • Substituted: \[ (2(0)−7)((0+9)) = (−7)(9) \]
   • Evaluate:
     • Step 1: \((−7)(9) = -63\)
     • Step 2: Check if \(-63 = 0\)?
   • Conclusion: False statement.

2. When \(x = 3\):

   • Substituted: \[ (2(3)−7)((3+9)) = (6−7)(12) \]
   • Evaluate:
     • Step 1: \( (−1)(12) = -12 \)
     • Step 2: Check if \(-12 = 0\)?
   • Conclusion: False statement.

3. When \(x = -9\):

   • Substituted: \[ (2(−9)−7)((−9+9)) = (−18−7)(0) \]
   • Evaluate:
     • Step 1: \((−25)(0) = 0\)
     • Step 2: Check if \(0 = 0\)?
   • Conclusion: True statement.

4. When \(x = 9\):

   • Substituted: \[ (2(9)−7)((9+9)) = (18−7)(18) \]
   • Evaluate:
     • Step 1: \( (11)(18) = 198 \)
     • Step 2: Check if \(198 = 0\)?
   • Conclusion: False statement.

Summary of the evaluations:

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

From the table, the only value that satisfies the equation is \(x = -9\).