Chapter 9 - Quadratic Functions and Equations - 9-5 Completing the Square - Practice and Problem-Solving Exercises - Page 564: 12

$4$

$q^2-4q+c$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=-4$ It will have discriminant, $d$ with formula : $d=b^2-4ac$ Since, $d=0$ for repeated root of the expression. Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$ To complete the square, plug in $a=1, b=-4$. Thus, $c=\dfrac{b^2}{4a}=\dfrac{(-4)^2}{4}=4$