What are the solutions to (x+3)2+4=0 (1 point) Responses −3±2i negative 3 plus or minus 2 i 3±4i 3 plus or minus 4 i 3±2i 3 plus or minus 2 i No solutions

Answer 1

To solve the equation \((x + 3)^2 + 4 = 0\), we start by isolating the square term.

1. Subtract 4 from both sides: \[ (x + 3)^2 = -4 \]

2. Now, take the square root of both sides: \[ x + 3 = \pm \sqrt{-4} \]

3. We know that \(\sqrt{-4} = 2i\), so we have: \[ x + 3 = \pm 2i \]

4. Now, solve for \(x\): \[ x = -3 \pm 2i \]

Thus, the solutions to the equation are: \[ -3 \pm 2i \]

From the provided responses, the correct answer is: \(-3 \pm 2i\) (which is "negative 3 plus or minus 2 i").