### Quadratic Equation Solution Selection **Problem Statement:** Select all solutions to \( (x - 2)^2 - 16 = 0 \) **Options:** - [ ] \( x = 6 \) - [ ] \( x = -2 \) - [ ] \( x = -6 \) - [ ] \( x = 2 \pm 4i \) - [ ] \( x = 2 \pm 2i \) - [ ] \( x = 2 \pm 2 \) - [ ] \( x = 2, -4 \) **Analysis:** To solve the equation \( (x - 2)^2 - 16 = 0 \), follow these steps: 1. Expand the squared term: \( (x - 2)^2 = x^2 - 4x + 4 \) 2. Substitute this back into the equation: \( x^2 - 4x + 4 - 16 = 0 \) \( x^2 - 4x - 12 = 0 \) 3. Factor the quadratic equation: \( (x - 6)(x + 2) = 0 \) 4. Solve for \( x \): - \( x - 6 = 0 \Rightarrow x = 6 \) - \( x + 2 = 0 \Rightarrow x = -2 \) Therefore, the solutions are \( x = 6 \) and \( x = -2 \). **Correct Answers:** - [ ] \( x = 6 \): True - [ ] \( x = -2 \): True - [ ] \( x = -6 \): False - [ ] \( x = 2 \pm 4i \): False - [ ] \( x = 2 \pm 2i \): False - [ ] \( x = 2 \pm 2 \): False - [ ] \( x = 2, -4 \): False **Online Practice Resource:** Access further practice questions via [MasteryConnect Student Portal](https://student.masteryconnect.com).