1. **State the problem:** Solve the quadratic equation $2x^2 - 10 = 26$ for $x$. 2. **Write the formula and rules:** To solve quadratic equations, we isolate the $x^2$ term and then take the square root of both sides. Remember to consider both positive and negative roots when taking the square root. 3. **Isolate the quadratic term:** $$2x^2 - 10 = 26$$ Add 10 to both sides: $$2x^2 - 10 + 10 = 26 + 10$$ $$2x^2 = 36$$ 4. **Divide both sides by 2 to solve for $x^2$:** $$\frac{2x^2}{\cancel{2}} = \frac{36}{\cancel{2}}$$ $$x^2 = 18$$ 5. **Take the square root of both sides:** $$x = \pm \sqrt{18}$$ 6. **Simplify the square root:** $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$$ 7. **Final solution:** $$x = \pm 3\sqrt{2}$$ This means the two solutions are $x = 3\sqrt{2}$ and $x = -3\sqrt{2}$.