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. Look at the given equation: \( (z - 4)^2 = 49 \). Notice that the equation is already written as a perfect square equal to a number.
2. Since the equation is in the form \( (\text{expression})^2 = \text{number} \), the Square-Root Property is the most straightforward method to solve it.
3. The Square-Root Property states that if \( a^2 = b \), then \( a = \pm \sqrt{b} \). Here, \( a \) corresponds to \( (z - 4) \) and \( b \) corresponds to 49.
4. Apply the Square-Root Property by taking the square root of both sides: \( z - 4 = \pm \sqrt{49} \).
5. From here, you can solve for \( z \) by isolating it: \( z = 4 \pm 7 \). This gives two possible solutions for \( z \).