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[tex]- \ \textgreater \ \ {2 x^{2} - 7x + 3} = x^{2} - \frac{7}{2}\ x + \frac{3}{2} \\ \\ - \ \textgreater \ x^{2} - 2 . \frac{7}{4}x + (\frac{7}{4})^{2} - (\frac{7}{4})^{2} + \frac{3}{2} \\ \\ - \ \textgreater \ ( x - \frac{7}{4} )^2 = \frac{49}{16} - \frac{24}{16} \\ \\ - \ \textgreater \ ( x - \frac{7}{4} ) = \sqrt{ \frac{25}{16} } = \frac{5}{4} \ or \ \frac{-5}{4} \\ \\ - \ \textgreater \ x = 3 \ or \ x = \frac{1}{2} [/tex]
Thus, the roots are x = 3 and x = 0.5
[tex]- \ \textgreater \ \ {2 x^{2} - 7x + 3} = x^{2} - \frac{7}{2}\ x + \frac{3}{2} \\ \\ - \ \textgreater \ x^{2} - 2 . \frac{7}{4}x + (\frac{7}{4})^{2} - (\frac{7}{4})^{2} + \frac{3}{2} \\ \\ - \ \textgreater \ ( x - \frac{7}{4} )^2 = \frac{49}{16} - \frac{24}{16} \\ \\ - \ \textgreater \ ( x - \frac{7}{4} ) = \sqrt{ \frac{25}{16} } = \frac{5}{4} \ or \ \frac{-5}{4} \\ \\ - \ \textgreater \ x = 3 \ or \ x = \frac{1}{2} [/tex]
Thus, the roots are x = 3 and x = 0.5
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