\(M=2x^2-5x+3\)
\(=2\left(x^2-\dfrac{5}{2}x+\dfrac{3}{2}\right)\)
\(=2\left(x^2-\dfrac{5}{4}x-\dfrac{5}{4}x+\dfrac{3}{2}\right)\)
\(=2\left[x\left(x-\dfrac{5}{4}\right)-\dfrac{5}{4}\left(x-\dfrac{5}{4}\right)-\dfrac{1}{16}\right]\)
\(=2\left[\left(x-\dfrac{5}{4}\right)^2-\dfrac{1}{16}\right]\)
\(=2\left(x-\dfrac{5}{4}\right)^2-\dfrac{1}{8}\)
Khi đó: \(2\left(x-\dfrac{5}{4}\right)^2=\dfrac{1}{8}\)
\(\Rightarrow\left(x-\dfrac{5}{4}\right)^2=\left(\dfrac{1}{4}\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}x-\dfrac{5}{4}=\dfrac{1}{4}\\x-\dfrac{5}{4}=-\dfrac{1}{4}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=1\end{matrix}\right.\).
Vậy ...
2x2 - 5x + 3 = 0
<=> 2x2 - 2x - 3x + 3 = 0
<=> 2x(x - 1) - 3(x - 1) = 0
<=> (x - 1)(2x - 3) = 0
<=> x - 1 = 0 hoặc 2x - 3 = 0
<=> x = 1 hoặc x = 1,5
