[tex] {x}^{2} + \frac{1}{2} x + \frac{1}{16} = {(x + \frac{1}{4} )}^{2} [/tex]
[tex] {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]
[tex] {(x + \frac{1}{4} )}^{2} = {x}^{2} + 2 \times x \times \frac{1}{4} + {( \frac{1}{4}) }^{2} [/tex]
[tex] {(x + \frac{1}{4} )}^{2} = {x}^{2} + \frac{2 \times 1}{4} x + \frac{ {1}^{2} }{ {4}^{2} } [/tex]
[tex] {(x + \frac{1}{4}) }^{2} = {x}^{2} + \frac{2}{4} x + \frac{1}{16} [/tex]
[tex] {(x + \frac{1}{4} )}^{2} = {x}^{2} + \frac{1}{2} x + \frac{1}{16} [/tex]
