Question

1. solve the equation using any method.

$4x^2 + 36 = 0$
options: 3i, 3, -9i, 9i, 3i, -3

Explanation:

Step1: Isolate the \(x^2\) term

Start with the equation \(4x^2 + 36 = 0\). Subtract 36 from both sides:
\(4x^2 = -36\)

Step2: Solve for \(x^2\)

Divide both sides by 4:
\(x^2 = \frac{-36}{4} = -9\)

Step3: Take the square root

Recall that \(\sqrt{-a} = i\sqrt{a}\) for real \(a > 0\). So, take the square root of both sides:
\(x = \pm\sqrt{-9} = \pm 3i\)

Answer:

\(3i\) and \(-3i\) (or \(3i\), \(-3i\))