Solve for $n$: $n^2-49=0$.

• A. $n=49$
• B. $n=7$ or $n=-7$
• C. $n=7$ only
• D. $n=\pm 49$

Answer: (B)

Verified step by step guidance

1. Start with the given equation: \(n^2 - 49 = 0\).
2. Recognize that this is a difference of squares, which can be factored using the identity \(a^2 - b^2 = (a - b)(a + b)\).
3. Rewrite the equation as \((n - 7)(n + 7) = 0\).
4. Set each factor equal to zero: \(n - 7 = 0\) and \(n + 7 = 0\).
5. Solve each equation to find the solutions: \(n = 7\) and \(n = -7\).