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.