Answer
Francisco was wrong because the quadratic formula works even when $c=0$.
Work Step by Step
RECALL:
The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula:
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
The given equation has:
$a=1, b=-8, c=0$
Substitute these values into the quadratic formula to obtain:
$x=\dfrac{-(-8) \pm \sqrt{(-8)^2-4(1)(0)}}{2(1)}
\\x=\dfrac{8\pm\sqrt{64-0}}{2}
\\x=\dfrac{8\pm\sqrt{64}}{2}
\\x=\dfrac{8\pm8}{2}
\\x_1=\dfrac{8-8}{2}=0
\\x_2=\dfrac{8+8}{2}=8$
Thus, the solution set is $\color{blue}{\left\{0, 8\right\}}$.
Francisco was wrong because the quadratic formula actually works for regardless of whether $c=0$ or not.
