To determine which value is a solution for the quadratic equation \( x^2 + 20x = 69 \), we first rearrange the equation into standard form:
\[ x^2 + 20x - 69 = 0 \]
Next, we will substitute each value of \( x \) into the equation and check if the left-hand side equals 0, thereby verifying if it is a solution.
Let's evaluate each of the given values:
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For \( x = -23 \): \[ (-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 529 - 529 = 0 \] True statement: Yes, \( x = -23 \) is a solution.
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For \( x = 0 \): \[ (0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69 \] True statement: No, \( x = 0 \) is not a solution.
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For \( x = 12 \): \[ (12)^2 + 20(12) - 69 = 144 + 240 - 69 = 144 + 240 - 69 = 315 \] True statement: No, \( x = 12 \) is not a solution.
Now compiling our findings, we see that only \( x = -23 \) satisfies the equation.
Thus, the answer is: Only \( x = -23 \) is in the solution set.
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