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)

Question

Responses

−4±2i
negative 4 plus or minus 2 i

16±2i
16 plus or minus 2 i

16±2i2–√
16 plus or minus 2 i Start Root 2 End Root

4±2i2–√

Answer 1

To solve the equation \( 2(x - 16)^2 = -8 \), we first isolate \((x - 16)^2\):

\[ (x - 16)^2 = \frac{-8}{2} = -4 \]

Next, we take the square root of both sides. Since the right side is negative, we will have complex solutions:

\[ x - 16 = \pm \sqrt{-4} = \pm 2i \]

Now, we can solve for \(x\) by adding 16 to both sides:

\[ x = 16 \pm 2i \]

Thus, the solution to the equation in standard form \( a \pm bi \) is:

\[ 16 \pm 2i \]

So, the correct response is:

16±2i 16 plus or minus 2 i