1. **State the problem:** Solve the quadratic equation $x^2 - 7x + 6 = 0$. 2. **Formula and rules:** To solve a quadratic equation of the form $ax^2 + bx + c = 0$, we can use factoring, completing the square, or the quadratic formula. Here, factoring is straightforward. 3. **Factor the quadratic:** Find two numbers that multiply to $6$ (the constant term) and add to $-7$ (the coefficient of $x$). These numbers are $-1$ and $-6$. 4. **Write the factored form:** $$x^2 - 7x + 6 = (x - 1)(x - 6) = 0$$ 5. **Solve for $x$:** Set each factor equal to zero: $$x - 1 = 0 \Rightarrow x = 1$$ $$x - 6 = 0 \Rightarrow x = 6$$ 6. **Final answer:** The solutions to the equation are $x = 1$ and $x = 6$.