Question

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

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