Which is the solution to the equation 2(x−16)2=−8 , re-expressed as a complex number in the standard form a±bi ?(1 point)

To solve the equation \( 2(x - 16)^2 = -8 \), we can start by isolating the term involving \( x \):

1. Divide both sides by 2: \[ (x - 16)^2 = -4 \]

2. Taking the square root of both sides gives: \[ x - 16 = \pm \sqrt{-4} \]

3. Since the square root of \(-4\) can be expressed in terms of imaginary numbers (using \( i \)), we have: \[ \sqrt{-4} = \sqrt{4} \cdot i = 2i \]

4. Therefore, we rewrite the equation as: \[ x - 16 = \pm 2i \]

5. Now, solve for \( x \): \[ x = 16 \pm 2i \]

Thus, the solutions to the equation in the standard form \( a \pm bi \) are:

\[ 16 \pm 2i \]

So, the correct response is:

16 ± 2i (or 16 plus or minus 2 i).