To check the solution of the quadratic equation \((2x - 7)(x + 9) = 0\) by substitution and evaluation, we substitute the given values into the equation. Let’s go through each one provided in the table:
Step 1: Substitute and Evaluate
-
Value: 0
- Substituted: \((2(0) - 7)(0 + 9) = (−7)(9)\)
- Evaluate: Step 1 gives \(-63\)
- Step 2: Is \(-63 = 0\)?
- Statement: False
-
Value: -9
- Substituted: \((2(-9) - 7)(-9 + 9) = (-18 - 7)(0)\)
- Evaluate: Step 1 gives \((-25)(0)\)
- Step 2: Is \(0 = 0\)?
- Statement: True
-
Value: 3
- Substituted: \((2(3) - 7)(3 + 9) = (6 - 7)(12)\)
- Evaluate: Step 1 gives \((-1)(12)\)
- Step 2: Is \(-12 = 0\)?
- Statement: False
-
Value: 9
- Substituted: \((2(9) - 7)(9 + 9) = (18 - 7)(18)\)
- Evaluate: Step 1 gives \((11)(18)\)
- Step 2: Is \(198 = 0\)?
- Statement: False
Conclusion
- For x = 0: False
- For x = -9: True
- For x = 3: False
- For x = 9: False
So, the complete table would look like this:
| Value | Substituted | Evaluate: Step 1 | Step 2 | True or False Statement? | |-------|----------------------------------|-------------------|-----------------------|---------------------------| | 0 | (2(0)−7)(0+9) = (−7)(9) | -63 | -63 = 0 | False | | -9 | (2(-9)−7)(-9+9) = (-25)(0) | 0 | 0 = 0 | True | | 3 | (2(3)−7)(3+9) = (-1)(12) | -12 | -12 = 0 | False | | 9 | (2(9)−7)(9+9) = (11)(18) | 198 | 198 = 0 | False |
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