[tex] - {x}^{2} + 10x + 5 \\ = - {x}^{2} + 10x - 25 + 5 + 25 \\ = - ( {x}^{2} - 10x + 25) + 30 \\ = \underbrace{ - {(x - 5)}^{2}}_{\leqslant 0} + 30 \\ \Rightarrow - {(x - 5)}^{2} + 30 \leqslant 30 \\ \Rightarrow Maximum \: value \: is \: 30 \: when \: x = 5[/tex]
