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


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Answer 1

Let's evaluate the quadratic equation \((2x−7)(x+9) = 0\) by substituting the given values into the equation and checking whether or not they satisfy the equation.

Evaluating Given Values

For Value 0:

1. Substitute: \(x = 0\) \[ (2(0)−7)(0+9) = (−7)(9) = -63 \]
2. Evaluate:
   • The equation equals \(-63\), which does not equal \(0\).
3. True or False Statement: \(-63 = 0\) False

For Value 3:

1. Substitute: \(x = 3\) \[ (2(3)−7)(3+9) = (6−7)(12) = (−1)(12) = -12 \]
2. Evaluate:
   • The equation equals \(-12\), which does not equal \(0\).
3. True or False Statement: \(-12 = 0\) False

For Value -9:

1. Substitute: \(x = -9\) \[ (2(-9)−7)(-9+9) = (−18−7)(0) = (−25)(0) = 0 \]
2. Evaluate:
   • The equation equals \(0\), which does equal \(0\).
3. True or False Statement: \(0 = 0\) True

For Value 9:

1. Substitute: \(x = 9\) \[ (2(9)−7)(9+9) = (18−7)(18) = (11)(18) = 198 \]
2. Evaluate:
   • The equation equals \(198\), which does not equal \(0\).
3. True or False Statement: \(198 = 0\) False

Summary of Results

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

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