\(x^2-x-3=0\)
\(\Leftrightarrow x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{13}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2-\dfrac{13}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=\dfrac{13}{4}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{2}=\sqrt{\dfrac{13}{4}}\\x-\dfrac{1}{2}=-\sqrt{\dfrac{13}{4}}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1+\sqrt{13}}{2}\\x=\dfrac{1-\sqrt{13}}{2}\end{matrix}\right.\)
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