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

Question

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 check the solutions for the quadratic equation \((2x - 7)(x + 9) = 0\), you'll substitute the given values for \(x\) and evaluate whether the equation holds true.

Let’s go through the values given in the table you provided, performing the steps for each value.

Value 0:

1. Substitute: \((2(0) - 7)(0 + 9) = 0\)
2. Evaluate: Step 1: \((-7)(9)\)
3. Step 2: \(-63 = 0\)
4. True or False Statement? False

Value 3:

1. Substitute: \((2(3) - 7)(3 + 9) = 0\)
2. Evaluate: Step 1: \((6 - 7)(12)\)
3. Step 2: \((-1)(12) = -12\)
4. True or False Statement? False

Value -9:

1. Substitute: \((2(-9) - 7)(-9 + 9) = 0\)
2. Evaluate: Step 1: \((-18 - 7)(0)\)
3. Step 2: \((-25)(0) = 0\)
4. True or False Statement? True

Value 9:

1. Substitute: \((2(9) - 7)(9 + 9) = 0\)
2. Evaluate: Step 1: \((18 - 7)(18)\)
3. Step 2: \((11)(18) = 198\)
4. True or False Statement? False

Summary Table:

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

The roots of the original equation \((2x - 7)(x + 9) = 0\) are found using the Zero Product Property, leading to the solutions \(x = \frac{7}{2}\) and \(x = -9\). Among the substituted values, only \(x = -9\) satisfies the equation.