To solve the equation \((x−3)^2−81=0\), we start by isolating the squared term:
\[ (x−3)^2 = 81 \]
Next, we take the square root of both sides:
\[ x - 3 = \pm 9 \]
Now we solve for \(x\) in both cases:
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\(x - 3 = 9\) \[ x = 9 + 3 = 12 \]
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\(x - 3 = -9\) \[ x = -9 + 3 = -6 \]
The solutions to the equation \((x−3)^2−81=0\) are \(x = 12\) and \(x = -6\).
From the provided answers, the solution that matches is:
12.