Which is the solution to the equation 2(x - 16)^2=-8, re-expressed as a complex number in the standard form a ± bi?
16±2i√2
-4±2i
4±2i√2
16±2i
To solve the equation 2(x - 16)^2 = -8, we can start by dividing both sides by 2:
(x - 16)^2 = -4
Next, we can take the square root of both sides to eliminate the square:
x - 16 = ±√(-4)
Since the square root of a negative number is not a real number, we know that the solution will be a complex number. We can rewrite √(-4) as 2i, where i represents the imaginary unit.
x - 16 = ±2i
Adding 16 to both sides, we have:
x = 16 ± 2i
Therefore, the solution to the equation 2(x - 16)^2 = -8, re-expressed as a complex number in the standard form a ± bi, is 16 ± 2i. The correct answer is 16 ± 2i.
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To find the complex solutions to the equation, we need to isolate the variable, x.
Given the equation: 2(x - 16)^2 = -8
First, divide both sides of the equation by 2: (x - 16)^2 = -4
Next, take the square root of both sides to remove the square: x - 16 = ±√(-4)
The square root of -4 is represented as ±2i, where i is the imaginary unit.
So, x - 16 = ±2i
Now, isolate the variable, x, by adding 16 to both sides: x = 16 ± 2i
Therefore, the solution to the equation is x = 16 ± 2i, which can be re-expressed in the standard form a ± bi.
So, the correct answer is 16±2i.