Question: The image contains the following text: \[ 2z^2 = 72 \] \[ z = \boxed{\phantom{0}} \]

The image contains the following text:

\[ 2z^2 = 72 \]

\[ z = \boxed{\phantom{0}} \]

Solution

The problem is to solve the equation \(2z^2 = 72\). First, divide both sides of the equation by 2 to simplify: \[ z^2 = \frac{72}{2} \] \[ z^2 = 36 \] Next, take the square root of both sides to solve for \(z\): \[ z = \sqrt{36} \] \[ z = 6 \quad \text{or} \quad z = -6 \] So, \( z = 6 \) or \( z = -6 \).