To determine which values are solutions to the quadratic equation \( x^2 + 20x = 69 \), we first need to rewrite the equation in standard form:
\[ x^2 + 20x - 69 = 0 \]
Next, we'll substitute each of the given values (-23, 0, and 12) into the equation and evaluate to see if the equation holds true (i.e., equals 0).
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For \( x = -23 \): \[ (-23)^2 + 20(-23) - 69 = 529 - 460 - 69 = 0 \] This is true: \( 0 = 0 \).
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For \( x = 0 \): \[ (0)^2 + 20(0) - 69 = 0 + 0 - 69 = -69 \] This is not true: \( -69 \neq 0 \).
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For \( x = 12 \): \[ (12)^2 + 20(12) - 69 = 144 + 240 - 69 = 315 \] This is not true: \( 315 \neq 0 \).
After evaluating all the options, we find that only \( x = -23 \) is a solution to the equation \( x^2 + 20x - 69 = 0 \).
Thus, the correct answer is: Only x = -23 is in the solution set.
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