Solve $2 x^{2} + x - 6$ by completing square method

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Solution

$2 x^{2} + x - 6$
Completing the square,
$\Rightarrow x^{2} + \frac{x}{2} - 3 = 0$
$\Rightarrow x^{2} + \frac{x}{2} + \frac{1}{16} - \frac{1}{16} - 3 = 0$
$\Rightarrow (x + \frac{1}{4})^{2} - \frac{49}{16} = 0$
$\Rightarrow (x + \frac{1}{4} - \frac{7}{4}) (x + \frac{1}{4} + \frac{7}{4}) = 0$
$\Rightarrow (x - \frac{3}{2}) (x + 2) = 0$
$\Rightarrow x = \frac{3}{2}, - 2$

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