Use the square root property to solve the equation. \[ (x-24)^{2}=19 \] The solution set is \( \{\square\} \). (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

To solve the equation \( (x-24)^{2}=19 \), we can apply the square root property, which states that if \( a^2 = b \), then \( a = \sqrt{b} \) or \( a = -\sqrt{b} \). First, we take the square root of both sides: \[ x-24 = \sqrt{19} \quad \text{or} \quad x-24 = -\sqrt{19}. \] Next, we isolate \( x \) by adding 24 to both sides in each equation: 1. \( x = 24 + \sqrt{19} \) 2. \( x = 24 - \sqrt{19} \) Thus, the solution set is \[ \{ 24 + \sqrt{19}, 24 - \sqrt{19} \}. \]