M = $\frac{10}{8}$x - 5$x^{2}$ - 1
⇔ M = - 5 (x² - $\frac{1}{4}$x + $\frac{1}{5}$ )
⇔ M = - 5 (x² - 2 . $\frac{1}{8}$x + $\frac{1}{64}$ - $\frac{63}{320}$)
⇔ M = - 5 (x² - 2 . $\frac{1}{8}$x + $\frac{1}{64}$ ) + $\frac{63}{320}$ . 5
⇔ M = - 5 ( x - $\frac{1}{8}$ ) + $\frac{63}{64}$ ≤ $\frac{63}{64}$
Dấu "=" xảy ra ⇔ x = $\frac{1}{8}$