1. Use the table to complete the statement.

Question

x Substituted Evaluate True Statement?
−34

−12

12



(1 point)
For the quadratic equation −2x2−3x+2=0
, complete the table by testing each of the given values to determine whether it is a solution. Identify which one of the values is in the solution set. Only x =

is in the solution set.
Question 2
2. Solve x2=289
by inspection. There are two real solutions. Enter the lesser number first.(2 points)
{
,
}
Question 3
3. Which values are in the solution set of the quadratic equation, −9+(x−3)2−4=−4
? Solve using square roots and choose all that apply.(2 points)
Responses

-22
-22

16
16

-8
-8

-2
-2

2
2

8
8

28
28

-10

Answer 1

Question 1

To determine which of the values is in the solution set for the quadratic equation \( -2x^2 - 3x + 2 = 0 \), we need to substitute each value of \( x \) into the equation and evaluate it.

Let's substitute each value:

For \( x = -34 \):

\[ -2(-34)^2 - 3(-34) + 2 = -2(1156) + 102 + 2 = -2312 + 102 + 2 = -2210 \quad (\text{Not } 0) \]

For \( x = -12 \):

\[ -2(-12)^2 - 3(-12) + 2 = -2(144) + 36 + 2 = -288 + 36 + 2 = -250 \quad (\text{Not } 0) \]

For \( x = 12 \):

\[ -2(12)^2 - 3(12) + 2 = -2(144) - 36 + 2 = -288 - 36 + 2 = -322 \quad (\text{Not } 0) \]

None of the values provided yield a true statement (i.e., evaluate to zero). Therefore: Only \( x = \text{none of these values} \) is in the solution set.

Question 2

To solve the equation \( x^2 = 289 \) by inspection:

We can find \( x \) by taking the square root of both sides: \[ x = \pm \sqrt{289} = \pm 17 \]

The two solutions are \( -17 \) and \( 17 \). Listing the lesser number first: { -17, 17 }

Question 3

To solve the equation \( -9 + (x - 3)^2 - 4 = -4 \):

1. Simplify the equation: \[ -9 + (x - 3)^2 - 4 = -4 \ (x - 3)^2 - 13 = -4 \quad \text{(adding 13 to both sides)} \ (x - 3)^2 = 9 \]

2. Taking the square root of both sides: \[ x - 3 = \pm 3 \]

So we have two cases:

• Case 1: \( x - 3 = 3 \) \ \( x = 6 \)

• Case 2: \( x - 3 = -3 \) \ \( x = 0 \)

Thus, the values in the solution set are: { 0, 6 }

From the provided responses, the values that are included in the solution set would be listed among the responses, which are not complete. Based on what we've calculated:

• 0 (not listed)
• 6 (not listed)

If given values include the correct integers with one of them as the answer, ensure that you compare between \( 0 \) and \( 6 \) if those numbers exist in your options provided.

Please verify against your list for exact matching values.