[tex]y=2x^2+5x+2\\\\2x^2+5x+2=0\\\\2x^2+4x+x+2=0\\\\2x(x+2)+1(x+2)=0\\\\(x+2)(2x+1)=0\iff x+2=0\ \vee\ 2x+1=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-2}\\\\2x+1=0\qquad\text{subtract 1 from both sides}\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\boxed{x=-\dfrac{1}{2}}\\\\Answer:\ \boxed{C.\ x=-\dfrac{1}{2},\ x=-2}[/tex]
