Solve the following quadratic equations by the method of perfect the square.
$3 x^{2} - 5 x + 2 = 0$

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Solution

$3 x^{2} - 5 x + 2 = 0 x^{2} - \frac{5}{3} x + \frac{2}{3} = 0 x^{2} - \frac{5}{3} x + \frac{25}{36} - \frac{25}{36} + \frac{2}{3} = 0 {(x - \frac{5}{3})}^{2} - \frac{1}{36} = 0 {(x - \frac{5}{3})}^{2} = \frac{1}{36} (x - \frac{5}{3}) = \pm \frac{1}{6} x = \frac{5}{3} \pm \frac{1}{6} x = \frac{11}{6}, \frac{9}{6}$

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