For the quadratic equation −2x2−3x+2=0

To determine whether each given value is a solution to the quadratic equation \(-2x^2 - 3x + 2 = 0\), we can substitute each value into the equation and check if it results in a true statement (i.e., the left-hand side equals 0).

Let's complete this task step-by-step:

1. **Rearrange the Equation**: Our original equation is already in standard form, so we can use it directly.

\[
-2x^2 - 3x + 2 = 0
\]

2. **Test Each Value**: We'll substitute each value into the left-hand side of the equation and check if it equals 0.

Here are a few example values to test:

- **Value 1: \(x = -2\)**
\[
-2(-2)^2 - 3(-2) + 2 = -2(4) + 6 + 2 = -8 + 6 + 2 = 0
\]
→ Equal to 0 (Solution)

- **Value 2: \(x = -1\)**
\[
-2(-1)^2 - 3(-1) + 2 = -2(1) + 3 + 2 = -2 + 3 + 2 = 3
\]
→ Not equal to 0 (Not a solution)

- **Value 3: \(x = 0\)**
\[
-2(0)^2 - 3(0) + 2 = 0 + 0 + 2 = 2
\]
→ Not equal to 0 (Not a solution)

- **Value 4: \(x = 1\)**
\[
-2(1)^2 - 3(1) + 2 = -2(1) - 3 + 2 = -2 - 3 + 2 = -3
\]
→ Not equal to 0 (Not a solution)

- **Value 5: \(x = 1.5\)**
\[
-2(1.5)^2 - 3(1.5) + 2 = -2(2.25) - 4.5 + 2 = -4.5 - 4.5 + 2 = -7
\]
→ Not equal to 0 (Not a solution)

3. **Summarize Results**: Based on our tests, the only value that satisfied the equation \(-2x^2 - 3x + 2 = 0\) is:

- **Solution Value**: \(x = -2\)

Now you can create a table to summarize the evaluations:

| Value of \(x\) | Result |
|----------------|--------------------------|
| -2 | Equals 0 (Solution) |
| -1 | Not equal to 0 |
| 0 | Not equal to 0 |
| 1 | Not equal to 0 |
| 1.5 | Not equal to 0 |

### Conclusion:
Only \(x = -2\) is a solution to the equation \(-2x^2 - 3x + 2 = 0\).