Answer:
See below
Step-by-step explanation:
[tex]2 {x}^{2} - 11x + 14 = 0 \\ dividing \: throughout \: by \: 2 \\ \\ \frac{ 2{x}^{2} }{2} - \frac{11}{2} x + \frac{14}{2} = \frac{0}{2} \\ \\ {x}^{2} - \frac{11}{2} x + 7 = 0 \\ \\ {x}^{2} - \frac{11}{2} x = - 7 \\ \\ {x}^{2} - 2 \times \frac{11}{4} x = - 7 \\ \\ {x}^{2} - 2 \times \frac{11}{4} x + \bigg(\frac{11}{4} \bigg)^{2} = \bigg(\frac{11}{4} \bigg)^{2} - 7 \\ \\ { \bigg(x - \frac{11}{4} \bigg )}^{2} = \frac{121}{16} - 7 \\ \\ { \bigg(x - \frac{11}{4} \bigg )}^{2} = \frac{121}{16} - 7 \\ \\ { \bigg(x - \frac{11}{4} \bigg )}^{2} = \frac{121 - 112}{16} \\ \\ {{ \bigg(x - \frac{11}{4} \bigg )}^{2} = \frac{9}{16} } \\ \\ \purple{{ \bigg(x + ( - \frac{11}{4}) \bigg )}^{2} = \frac{9}{16} }[/tex]
