Đáp án+Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 2m^{2} +m+1=2\left( m^{2} +\frac{1}{2} m+\frac{1}{2}\right)\\ =2\left( m^{2} +2.\frac{1}{4} m+\frac{1}{16} +\frac{7}{16}\right)\\ =2\left( m^{2} +2.\frac{1}{4} m+\frac{1}{16}\right) +2.\frac{7}{16}\\ =2\left( m^{2} +2.\frac{1}{4} m+\frac{1}{16}\right) +\frac{7}{8}\\ =2\left( m+\frac{1}{4}\right)^{2} +\frac{7}{8} \end{array}$