Solve each of the following equation by using the method of completing the square:
$3 x^{2} + x - 2 = 0$ ?

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Solution

$3 x^{2} - 2 x = 2$ Divide both sides by
$3 x^{2} - \frac{2 x}{3} = \frac{2}{3}$
$x^{2} - \frac{2 x}{3} + \frac{1}{9} = \frac{2}{3} + \frac{1}{9} = \frac{7}{9}$
$(x - \frac{1}{3})^{2} = \frac{7}{9}$
$x - \frac{1}{3} = \pm \sqrt{\frac{7}{9}}$
$x = \frac{1}{3} \pm \sqrt{\frac{7}{9}}$

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