Which of the following is a solution?

Question

(X - 3)^2 - 81 = 0
A. -3
B. 12
C. -12
D. 3

Answer 1

To solve the equation \((X - 3)^2 - 81 = 0\), we can first rearrange it as follows:

\[ (X - 3)^2 = 81 \]

Next, we take the square root of both sides:

\[ X - 3 = 9 \quad \text{or} \quad X - 3 = -9 \]

Now, we can solve for \(X\) in both cases:

1. For \(X - 3 = 9\):

\[ X = 9 + 3 = 12 \]

2. For \(X - 3 = -9\):

\[ X = -9 + 3 = -6 \]

This gives us the solutions \(X = 12\) and \(X = -6\).

Now, we need to check which of the answer options provided is a solution. The options are: A. -3
B. 12
C. -12
D. 3

The only solution that matches one of the options is:

B. 12

Thus, the correct answer is B. 12.