2x2 -3x -5 =0
2x2 - 5x +2x -5 =0
(2x2 + 2x) - (5x+5)=0
2x (x +1) -5(x +1) =0
(x+1)(2x -5)=0
⇔\(\left\{{}\begin{matrix}x+1=0\\2x-5=0\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}x=-1\\2x=5\end{matrix}\right.\)⇒\(\left\{{}\begin{matrix}x=-1\\x=\dfrac{5}{2}\end{matrix}\right.\)
Vậy x = -1 ; x =\(\dfrac{5}{2}\)
\(2x^2-3x-5=0\)
\(\Leftrightarrow2x^2+2x-5x-5=0\)
\(\Leftrightarrow\left(2x-5\right)\left(x+1\right)=0\)
\(\Leftrightarrow|^{2x-5=0}_{x+1=0}\) \(\left\{{}\begin{matrix}x=\dfrac{5}{2}\\x=-1\end{matrix}\right.\)
\(2x^2-3x-5=0\)
\(\Leftrightarrow2\left(x^2-\dfrac{3}{2}x-\dfrac{5}{2}\right)=0\)
\(\Leftrightarrow x^2-\dfrac{3}{2}x-\dfrac{5}{2}=0\)
\(\Leftrightarrow x^2-2.x.\dfrac{3}{4}+\left(\dfrac{3}{4}\right)^2-\dfrac{49}{16}=0\)
\(\Leftrightarrow\left(x-\dfrac{3}{4}\right)^2=\dfrac{49}{16}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{3}{4}=\dfrac{7}{4}\\x-\dfrac{3}{4}=-\dfrac{7}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-1\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=\dfrac{5}{2}\\x=-1\end{matrix}\right.\)
