Which would be the most appropriate method to solve the following equation?
$(z-4{)}^2=49$

• A. Factoring
• B. Square-Root Property
• C. Quadratic Formula
• D. Complete the Square

Answer: (B)

Verified step by step guidance

1. Identify the given equation: \( (z - 4)^2 = 49 \). This is a quadratic equation written in a form where a binomial is squared and set equal to a number.
2. Recognize that the equation is already in the form \( (expression)^2 = number \), which is ideal for applying the Square-Root Property.
3. Recall the Square-Root Property: If \( A^2 = B \), then \( A = \pm \sqrt{B} \). This allows you to take the square root of both sides to solve for the variable inside the parentheses.
4. Apply the Square-Root Property to get \( z - 4 = \pm \sqrt{49} \), which simplifies to \( z - 4 = \pm 7 \).
5. From here, solve the two resulting linear equations: \( z - 4 = 7 \) and \( z - 4 = -7 \) to find the values of \( z \).