If you were solving the equation (x-8)^2=-36 by taking the square root of both sides, which of the following would be the next step? A. x-8= +-6i B. x-8=6i C. x+8=6i D. x-8= +-6
Mathematics · College · Sun Jan 24 2021
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The correct next step in solving the equation (x-8)^2=-36 by taking the square root of both sides is A. x-8 = ±6i.
Here's why: When you take the square root of both sides of the equation (x-8)^2=-36, you must remember that taking the square root of a squared expression gives you both the positive and the negative square root. Also, the square root of a negative number introduces the imaginary unit i, where i is defined as the square root of -1.
So taking the square root of both sides gives us:
√((x-8)^2) = √(-36)
This simplifies to:
x - 8 = ±√(-36)
Since √(-36) is √(36) * √(-1), which is 6i (because √(36)=6 and √(-1)=i), we get:
x - 8 = ±6i