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

16±2i
16 plus or minus 2 i

−4±2i
negative 4 plus or minus 2 i

4±2i2–√
4 plus or minus 2 i Start Root 2 End Root

16±2i2–√
16 plus or minus 2 i Start Root 2 End Root
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Answer 1

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

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

2. Next, take the square root of both sides. Remember that taking the square root of a negative number involves imaginary units: \[ x - 16 = \pm \sqrt{-4} = \pm 2i \]

3. Now, solve for \( x \) by adding 16 to both sides: \[ x = 16 \pm 2i \]

Thus, the solution to the equation in standard complex number form \( a \pm bi \) is: \[ 16 \pm 2i \]

The correct response from your options is: 16 ± 2i.