What is the exact solution to the equation \( (x+4)^{2}-16=-4 \) ? \( x=2 \sqrt{3} \) \( x=4 \sqrt{3} \) \( x=2 \pm 1 \sqrt{3} \) \( x=-2 \pm 1 \sqrt{3} \) \( x=6 \sqrt{3} \) \( x= \pm 4 \) \( x=-4 \pm 2 \sqrt{3} \) \( x=4 \pm 2 \sqrt{3} \) \( x= \pm 2 \sqrt{3} \) \( x= \pm 2 \)

To solve the equation \( (x + 4)^2 - 16 = -4 \), follow these steps: 1. **Start with the original equation:** \[ (x + 4)^2 - 16 = -4 \] 2. **Add 16 to both sides to isolate the squared term:** \[ (x + 4)^2 = 12 \] 3. **Take the square root of both sides:** \[ x + 4 = \pm \sqrt{12} \] Simplify \(\sqrt{12}\): \[ \sqrt{12} = 2\sqrt{3} \] So, \[ x + 4 = \pm 2\sqrt{3} \] 4. **Subtract 4 from both sides to solve for \(x\):** \[ x = -4 \pm 2\sqrt{3} \] **Therefore, the exact solutions are:** \[ x = -4 + 2\sqrt{3} \quad \text{and} \quad x = -4 - 2\sqrt{3} \] Looking at the provided options, the correct answer matches: **\( x = -4 \pm 2\sqrt{3} \)** **Answer:** \( x=-4 \pm 2 \sqrt{3} \)