To determine which values from the table are solutions to the quadratic equation \(-2x^2 - 3x + 2 = 0\), we need to substitute each value of \(x\) into the equation and evaluate whether the equation holds true (i.e., if it equals zero).
Let's evaluate each of the values:
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For \(x = -34\):
\[ -2(-34)^2 - 3(-34) + 2 \] \[ = -2(1156) + 102 + 2 \] \[ = -2312 + 102 + 2 \] \[ = -2312 + 104 = -2208 \quad (\text{False Statement}) \]
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For \(x = -12\):
\[ -2(-12)^2 - 3(-12) + 2 \] \[ = -2(144) + 36 + 2 \] \[ = -288 + 36 + 2 \] \[ = -288 + 38 = -250 \quad (\text{False Statement}) \]
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For \(x = 12\):
\[ -2(12)^2 - 3(12) + 2 \] \[ = -2(144) - 36 + 2 \] \[ = -288 - 36 + 2 \] \[ = -288 - 34 = -322 \quad (\text{False Statement}) \]
Based on our calculations, none of the values yield a true statement where the equation equals zero. Thus, it seems that no values from the table are in the solution set.
Hence, you can complete the statement as follows:
Only \(x = \textbf{None}\) is in the solution set.
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