Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]q^2-\dfrac{1}{4}q=q^2-2\cdot \dfrac{1}{8}\cdot x=(q-\dfrac{1}{8})^2-\dfrac{1}{8^2}\\\\=\boxed{(q-\dfrac{1}{8})^2-\dfrac{1}{64}}\\\\\text{ We need to add } \dfrac{1}{64} \text{ to complete the square.}\\\\[/tex]
[tex]\Large \boxed{\sf \ \ q^2-\dfrac{1}{4}q+\dfrac{1}{64}=(q-\dfrac{1}{8})^2 \ \ }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
