[tex] x^2- \dfrac{1}{4} x+k[/tex]
To make the expression a perfect square, we always add [tex]( \dfrac{b}{2} )^2[/tex]:
[tex]k = (\dfrac{1}{4} \div 2)^2[/tex]
[tex]k = (\dfrac{1}{4} \times \dfrac{1}{2} )^2[/tex]
[tex]k = (\dfrac{1}{8} )^2[/tex]
[tex]k = \dfrac{1}{64}[/tex]
