Solve the equation by finding square roots.4a Superscript 2plus64equals0Question content area bottomPart 1Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.A.aequalsenter your response here ​(Simplify your answer. Use a comma to separate answers as​ needed.)B.The solution is not a real number.

To solve the equation \(4a^2 + 64 = 0\), we can start by isolating \(a^2\).

1. Subtract 64 from both sides: \[ 4a^2 = -64 \]

2. Divide both sides by 4: \[ a^2 = -16 \]

Next, to find the values of \(a\), we take the square root of both sides. However, since we are taking the square root of a negative number, we will get complex solutions:

3. Taking the square root: \[ a = \pm \sqrt{-16} \]

Using the property that \(\sqrt{-1} = i\), we can rewrite the equation: \[ a = \pm 4i \]

Thus, the solutions are: \[ a = 4i, -4i \]

So, the correct choice is:

A. \(a = 4i, -4i\) (Simplified answer: \(4i, -4i\))