Question

Question

Which of the following is a solution?

(x−3)2−81=0


(1 point)
Responses

3
3

-12
-12

-3
-3

12

Answer 1

To solve the equation $(x-3{)}^2-81=0$, we can start by rewriting it:

$$(x-3{)}^2=81$$

Next, we take the square root of both sides, keeping in mind that there will be both positive and negative square roots:

$$x-3=9\text{or}x-3=-9$$

Now, we solve each equation separately:

1. For $x-3=9$:

$$x=9+3=12$$

2. For $x-3=-9$:

$$x=-9+3=-6$$

Thus, the solutions to the equation are:

$$x=12\text{and}x=-6$$

From the provided options, the only solution given is:

12

Therefore, the correct answer is 12.