Question

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.

Answer 1

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: \(4i, -4i\))