Which of the following is a solution?

(x−3)2−81=0


(1 point)
Responses

-3
-3

12
12

-12
-12

3

1 answer

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:

  1. \(x - 3 = 9\) \[ x = 9 + 3 = 12 \]

  2. \(x - 3 = -9\) \[ x = -9 + 3 = -6 \]

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.