Which of these potential solutions make the equation x2+9=0 true?(1 point)

Question

Responses

{−3,−3i}
left brace negative 3 comma negative 3 i right brace

{3,−3}
left brace 3 comma negative 3 right brace

{ }
left brace right brace

{3i,−3i}

Answer 1

To solve the equation \( x^2 + 9 = 0 \), we can start by rearranging the equation:

\[ x^2 = -9 \]

Next, taking the square root of both sides, we get:

\[ x = \pm \sqrt{-9} \]

Since \(\sqrt{-9} = \sqrt{9} \cdot \sqrt{-1} = 3i\), we find:

\[ x = \pm 3i \]

This means the solutions to the equation are:

\[ x = 3i \quad \text{and} \quad x = -3i \]

Therefore, the correct response that makes the equation true is:

\({3i, -3i}\)