Final answer:
The student's question pertains to solving quadratic equations by completing the square, a method that involves creating a perfect square trinomial to simplify finding the roots.
Step-by-step explanation:
The question involves solving quadratic equations using the method of completing the square. This mathematical technique is an alternative to the quadratic formula and can often simplify the process of finding the roots of a quadratic equation. For a general quadratic equation of the form ax²+bx+c = 0, completing the square involves creating a perfect square trinomial on one side of the equation, which can be more easily solved. For example, given the equation x²-4x+8=0, one would complete the square by adding and subtracting the square of half the coefficient of x, which is (-4/2)² = 4, resulting in (x-2)²=0, thereby finding the roots of the equation.