Answer: D. x = 32 and x = 0
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Explanation:
Think of x-16 as y. In other words, let y = x-16
We have (x-16)^2 = 256 become y^2 = 256.
Solve for y to get y = 16 or y = -16. You apply the square root to both sides. Don't forget about the plus/minus. This is because (-16)^2 = (-16)*(-16) = 256. We square the negative as well.
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If y = 16, then y = x-16 solves for x to get
y = x-16
16 = x-16
x-16 = 16
x = 16+16
x = 32 is one solution
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Plug in y = -16 and isolate x
y = x-16
x-16 = y
x-16 = -16
x = -16+16
x = 0 is the other solution
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We can check each answer by plugging them back into the original equation
Let's try x = 0
(x-16)^2 = 256
(0-16)^2 = 256
(-16)^2 = 256
256 = 256 ... works
Now try x = 32
(x-16)^2 = 256
(32-16)^2 = 256
(16)^2 = 256
256 = 256 ... also works; both answers have been confirmed
