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

Question

Responses

{ }
left brace right brace

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

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

{−3,−3i}

Answer 1

To solve the equation \(x^2 + 9 = 0\), we first isolate \(x^2\):

\[ x^2 = -9 \]

Next, we take the square root of both sides. Remember that the square root of a negative number introduces an imaginary unit \(i\):

\[ x = \pm \sqrt{-9} = \pm \sqrt{9} \cdot i = \pm 3i \]

Thus, the solutions to the equation are:

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

From the options given, the correct set of solutions is:

\[ {3i, -3i} \]

So the right response is:

{3i, −3i}.