1. **State the problem:** Solve the quadratic equation $$x^2 - 6x - 10 = 0$$ for $x$ and give each answer correct to 2 decimal places. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients. 3. **Identify coefficients:** Here, $a = 1$, $b = -6$, and $c = -10$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-6)^2 - 4 \times 1 \times (-10) = 36 + 40 = 76$$ 5. **Apply the quadratic formula:** $$x = \frac{-(-6) \pm \sqrt{76}}{2 \times 1} = \frac{6 \pm \sqrt{76}}{2}$$ 6. **Simplify the square root:** $$\sqrt{76} = \sqrt{4 \times 19} = 2\sqrt{19}$$ 7. **Rewrite the expression:** $$x = \frac{6 \pm 2\sqrt{19}}{2}$$ 8. **Cancel common factor 2:** $$x = \frac{\cancel{2} \times 3 \pm \cancel{2} \times \sqrt{19}}{\cancel{2}} = 3 \pm \sqrt{19}$$ 9. **Calculate approximate values:** $$\sqrt{19} \approx 4.36$$ 10. **Final answers:** $$x_1 = 3 + 4.36 = 7.36$$ $$x_2 = 3 - 4.36 = -1.36$$ **Answer:** The solutions to the equation are $$x = 7.36$$ and $$x = -1.36$$ (rounded to 2 decimal places).