\(E=2x^2+8x+15\)
\(=\left(2x^2+8x+8\right)+7\)
\(=2\left(x^2+2.2.x+2^2\right)+7\)
\(=2\left(x+2\right)^2+7\)
\(2\left(x+2\right)^2\ge0\)
\(\Rightarrow2\left(x+2\right)^2+7\ge7\)
\(\Leftrightarrow Min_E=7\Leftrightarrow x+2=0\)
\(\Leftrightarrow x=-2\)
Vậy ...