Scope of quadratic formula

Description of Bottleneck

When using the quadratic formula in the form $x={\frac {1}{2}}(-p\pm {\sqrt {p^{2}-4q}}$

students don’t check whether the the quadratic equation to be solved is in the form

$x^{2}+px+q=0$,

i.e. that the x^2-coefficient is equal to unity.

That is to say, students don't check whether the prerequisites for the applicability of this formula apply.

This bottleneck is a special case of Scope of formula.