Ayana and Leah were trying to solve the equation: \( (x-5)^{2}+4=16 \) Ayana said, "I'll take the square root of both sides and rewrite the equation as \( (x-5)+2=4 \). Then I'll solve for \( x \)." Leah said, "IIl isolate \( (x-5)^{2} \) by subtracting 4 from both sides of the equation. Then l'll solve by taking the square root." Whose solution strategy would work?

Ayana’s strategy is not correct. The mistake is that you cannot take the square root of a sum term-by-term. That is, √[(x – 5)² + 4] is not the same as √[(x – 5)²] + √4. Leah’s strategy, on the other hand, is correct. Here’s how it works: 1. Start with the original equation:   (x – 5)² + 4 = 16 2. Subtract 4 from both sides to isolate the squared term:   (x – 5)² = 12 3. Then take the square root of both sides. Remember to consider both the positive and negative roots:   x – 5 = ±√12 4. Simplify √12 (if needed, as 2√3):   x – 5 = ±2√3 5. Finally, solve for x by adding 5 to both sides:   x = 5 ± 2√3 Thus, Leah’s approach correctly solves the equation, while Ayana’s does not.