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:
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Rearrange the Equation: Our original equation is already in standard form, so we can use it directly.
\[ -2x^2 - 3x + 2 = 0 \]
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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:
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Value 1: \(x = -2\) \[ -2(-2)^2 - 3(-2) + 2 = -2(4) + 6 + 2 = -8 + 6 + 2 = 0 \] → Equal to 0 (Solution)
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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)
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Value 3: \(x = 0\) \[ -2(0)^2 - 3(0) + 2 = 0 + 0 + 2 = 2 \] → Not equal to 0 (Not a solution)
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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)
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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)
- 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 \(-2x^2 - 3x + 2 = 0\).