Question

2x²+3x+1=0

Answer 1

\(\Leftrightarrow2x^2+2x+x+1=0\)

\(\Leftrightarrow2x\left(x+1\right)+\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(2x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\2x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-\dfrac{1}{2}\end{matrix}\right.\)

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Answer 2

2x² + 3x + 1 =0

<=> (2x² + 2x) + (x + 1) = 0

<=> 2x(x + 1) + (x+1) = 0

<=> (2x+1)(x+1) = 0

<=> \(\left[{}\begin{matrix}x=\dfrac{-1}{2}\\x=-1\end{matrix}\right.\)

KL: x \(\in\left\{\dfrac{-1}{2};-1\right\}\)