1. **State the problem:** Solve the quadratic equation $x^2 - 1x - 6 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=-1$, and $c=-6$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-1)^2 - 4 \times 1 \times (-6) = 1 + 24 = 25$$ 4. **Apply the quadratic formula:** $$x = \frac{-(-1) \pm \sqrt{25}}{2 \times 1} = \frac{1 \pm 5}{2}$$ 5. **Find the two solutions:** - For the plus sign: $$x = \frac{1 + 5}{2} = \frac{6}{2} = 3$$ - For the minus sign: $$x = \frac{1 - 5}{2} = \frac{\cancel{\, -4}}{\cancel{2}} = -2$$ 6. **Final answer:** The solutions to the equation are $x=3$ and $x=-2$.