Express $x^{2}-5x+\dfrac {1}{4}$ in the form $\left( x-a\right) ^{2}-b$

$\left( x-a\right) ^{2}-b$ is equal to $x^{2}-2ax+a^{2}-b$

Expanding $[x^{2}-5x)]$ we get $[x^{2}-2 \times x \times \dfrac{5}{2}+ {(\dfrac{5}{2})}^2] - {(\dfrac{5}{2})}^2$

$\therefore x^{2}-5x+\dfrac {1}{4}$ can be written as

$[x^{2}-2 \times x \times \dfrac{5}{2}+ {(\dfrac{5}{2})}^2] - {(\dfrac{5}{2})}^2+\dfrac {1}{4}$

or $({x - \dfrac{5}{2})}^{2} - \dfrac{25}{4}+ \dfrac{1}{4}$

or $({x - \dfrac{5}{2})}^{2} - \dfrac{25-1}{4}$

or $({x - \dfrac{5}{2})}^{2} - \dfrac{24}{4}$

or $({x - \dfrac{5}{2})}^{2} - 6$

$\therefore x^{2}-5x+\dfrac {1}{4}$ can be expressed the form $\left( x-a\right) ^{2}-b$ as

$\bold{({x - \dfrac{5}{2})}^{2} - 6}$ where $a=\dfrac{5}{2}$ and $b=6$