Đáp án:
$\begin{array}{l}
M = {\left( {2x + 5} \right)^2} + 2x\left( {3x - 4} \right) - \left( {{x^2} + 22} \right)\\
= 4{x^2} + 20x + 25 + 6{x^2} - 8x - {x^2} - 22\\
= 9{x^2} + 12x + 3\\
= {\left( {3x} \right)^2} + 2.3x.2 + 4 - 1\\
= {\left( {3x + 2} \right)^2} - 1\\
Do:{\left( {3x + 2} \right)^2} \ge 0\forall x\\
\Rightarrow {\left( {3x + 2} \right)^2} - 1 \ge - 1\forall x\\
\Rightarrow M \ge - 1\\
\Rightarrow GTNN:M = - 1 \Leftrightarrow x = - \frac{2}{3}
\end{array}$
Vậy x= -2/3 thì M đạt GTNN M =-1
