Question

Please help me rewrite the equation by completing the square

Answer 1

See below

Explanation:

`2 {x}^(2) - 11x + 14 = 0 \\ dividing \: throughout \: by \: 2 \\ \\ \frac{ 2{x}^(2) }{2} - (11)/(2) x + (14)/(2) = (0)/(2) \\ \\ {x}^(2) - (11)/(2) x + 7 = 0 \\ \\ {x}^(2) - (11)/(2) x = - 7 \\ \\ {x}^(2) - 2 * (11)/(4) x = - 7 \\ \\ {x}^(2) - 2 * (11)/(4) x + \bigg((11)/(4) \bigg)^(2) = \bigg((11)/(4) \bigg)^(2) - 7 \\ \\ { \bigg(x - (11)/(4) \bigg )}^(2) = (121)/(16) - 7 \\ \\ { \bigg(x - (11)/(4) \bigg )}^(2) = (121)/(16) - 7 \\ \\ { \bigg(x - (11)/(4) \bigg )}^(2) = (121 - 112)/(16) \\ \\ {{ \bigg(x - (11)/(4) \bigg )}^(2) = (9)/(16) } \\ \\ \purple{{ \bigg(x + ( - (11)/(4)) \bigg )}^(2) = (9)/(16) }`