To determine which value(s) from the table are solutions to the equation \(x^2 + 20x = 69\), we can rearrange the equation to standard form:
\[ x^2 + 20x - 69 = 0 \]
Now we will evaluate whether each of the given values (-23, 0, 12) is a solution by substituting them into the equation to see if the left side equals 0.
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For \(x = -23\): \[ (-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0 \] This simplifies to: \[ 0 = 0 \] So, \(x = -23\) is a solution.
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For \(x = 0\): \[ (0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69 \] This simplifies to: \[ -69 \neq 0 \] So, \(x = 0\) is not a solution.
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For \(x = 12\): \[ (12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315 \] This simplifies to: \[ 315 \neq 0 \] So, \(x = 12\) is not a solution.
Thus, the only value from the given list that is in the solution set is:
Only \(x = -23\) is in the solution set.