1. The problem is to find an alternative solution to a previously solved problem that yields the same answer. 2. Since the original problem is not specified, let's consider a common algebraic example: solving the quadratic equation $x^2 - 5x + 6 = 0$. 3. The standard method is factoring: $x^2 - 5x + 6 = (x - 2)(x - 3) = 0$, so $x = 2$ or $x = 3$. 4. An alternative method is using the quadratic formula: For $ax^2 + bx + c = 0$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. Here, $a=1$, $b=-5$, and $c=6$. Substitute these values: $$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4 \cdot 1 \cdot 6}}{2 \cdot 1} = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2}$$ 6. Calculate the two solutions: - $x = \frac{5 + 1}{2} = 3$ - $x = \frac{5 - 1}{2} = 2$ 7. Both methods yield the same solutions $x=2$ and $x=3$. This demonstrates an alternative solution method with the same answer.