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