1. **State the problem:** Solve for $x$ in the equation $3x^2 = 75$. 2. **Formula and rules:** To solve quadratic equations of the form $ax^2 = b$, isolate $x^2$ by dividing both sides by $a$, then take the square root of both sides. Remember, taking the square root yields two solutions: positive and negative. 3. **Intermediate work:** - Divide both sides by 3: $$x^2 = \frac{75}{3} = 25$$ - Take the square root of both sides: $$x = \pm \sqrt{25}$$ - Simplify the square root: $$x = \pm 5$$ 4. **Answer:** The solutions are $x = 5$ and $x = -5$. This completes the solution for the first problem.