\( (x+1)^{2}=4 \) (픈 2) What are the solutions to the equation? Choose 1 answer: (A) \( x=1 \pm \sqrt{2} \) (B) \( x=-1 \pm \sqrt{2} \) (C) \( x=1 \pm 2 \) (D) \( x=-1 \pm 2 \)

To solve the equation \( (x+1)^{2} = 4 \), you take the square root of both sides, giving you \( x+1 = \pm 2 \). This leads to two cases: 1. \( x + 1 = 2 \) ⇒ \( x = 1 \) 2. \( x + 1 = -2 \) ⇒ \( x = -3 \) So the solutions to the equation are \( x = 1 \) and \( x = -3 \). Looking at the answer choices you provided, the correct formulation would be represented more closely to option (D): \( x=-1 \pm 2 \), which works out to the correct solutions when you consider both sides of the plus-minus. To summarize: The possible values of \( x \) are \( -1 + 2 = 1 \), and \( -1 - 2 = -3 \). Therefore, the answer is (D) \( x=-1 \pm 2 \). Give a celebration cheer for those pesky mathematical equations—another one solved! 🎉