1. **State the problem:** We need to solve the equation $$25 = 4z^2$$ for $z$. 2. **Formula and rules:** To solve for $z$, isolate $z^2$ by dividing both sides by 4. 3. **Isolate $z^2$:** $$25 = 4z^2$$ Divide both sides by 4: $$\frac{25}{\cancel{4}} = \frac{4z^2}{\cancel{4}} \implies z^2 = \frac{25}{4}$$ 4. **Solve for $z$:** Take the square root of both sides: $$z = \pm \sqrt{\frac{25}{4}} = \pm \frac{\sqrt{25}}{\sqrt{4}} = \pm \frac{5}{2}$$ 5. **Interpretation:** The solutions are $z = \frac{5}{2}$ and $z = -\frac{5}{2}$. 6. **Answer for Part A:** The correct choice is C) $\frac{5}{2}$ and $-\frac{5}{2}$. 7. **Part B:** True or False: To verify a solution, substitute it back into $4z^2$ and check if the result equals 25. This is true because substituting the solution into the original expression confirms correctness. **Final answers:** - Part A: C - Part B: True