1. **Problem statement:** Solve the equation $x^2 = \frac{25}{4}$ for $x$. 2. **Formula and rules:** To solve $x^2 = a$, take the square root of both sides: $x = \pm \sqrt{a}$. 3. **Solution:** $$x = \pm \sqrt{\frac{25}{4}}$$ 4. **Simplify the square root:** $$x = \pm \frac{\sqrt{25}}{\sqrt{4}} = \pm \frac{5}{2}$$ 5. **Final answer:** $$x = \pm \frac{5}{2}$$ 1. **Problem statement:** Solve the equation $2x^2 = 22$ for $x$. 2. **Formula and rules:** Divide both sides by 2 to isolate $x^2$. 3. **Divide both sides:** $$\cancel{2}x^2 = \frac{22}{\cancel{2}}$$ $$x^2 = 11$$ 4. **Take square root:** $$x = \pm \sqrt{11}$$ 5. **Final answer:** $$x = \pm \sqrt{11}$$ 1. **Problem statement:** Solve the equation $7x^2 = 16$ for $x$. 2. **Formula and rules:** Divide both sides by 7 to isolate $x^2$. 3. **Divide both sides:** $$\cancel{7}x^2 = \frac{16}{\cancel{7}}$$ $$x^2 = \frac{16}{7}$$ 4. **Take square root:** $$x = \pm \sqrt{\frac{16}{7}}$$ 5. **Simplify the square root:** $$x = \pm \frac{\sqrt{16}}{\sqrt{7}} = \pm \frac{4}{\sqrt{7}}$$ 6. **Final answer:** $$x = \pm \frac{4}{\sqrt{7}}$$