1. **State the problem:** Solve the quadratic equation $12x^2 = 25$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero. $$12x^2 - 25 = 0$$ 3. **Isolate $x^2$:** Add 25 to both sides and then divide both sides by 12. $$12x^2 = 25$$ $$\cancel{12}x^2 = \cancel{12}\frac{25}{12}$$ $$x^2 = \frac{25}{12}$$ 4. **Take the square root of both sides:** Remember to consider both positive and negative roots. $$x = \pm \sqrt{\frac{25}{12}}$$ 5. **Simplify the square root:** $$x = \pm \frac{\sqrt{25}}{\sqrt{12}} = \pm \frac{5}{\sqrt{12}}$$ 6. **Rationalize the denominator:** Multiply numerator and denominator by $\sqrt{12}$. $$x = \pm \frac{5}{\sqrt{12}} \times \frac{\sqrt{12}}{\sqrt{12}} = \pm \frac{5\sqrt{12}}{12}$$ 7. **Simplify $\sqrt{12}$:** $$\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$$ 8. **Final simplified form:** $$x = \pm \frac{5 \times 2 \sqrt{3}}{12} = \pm \frac{10 \sqrt{3}}{12} = \pm \frac{5 \sqrt{3}}{6}$$ **Answer:** $$x = \pm \frac{5 \sqrt{3}}{6}$$