Solve the following quadratic equation by completing the square: $2 x^{2} + 5 x - 3 = 0$

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Solution

Given quadratic equation is:

$2 x^{2} + 5 x - 3 = 0$

$x^{2} + \frac{5}{2} x - \frac{3}{2} = 0$

$x^{2} + \frac{5}{2} x - \frac{3}{2} + \frac{25}{16} - \frac{25}{16} = 0$

$x^{2} + \frac{5}{2} x + \frac{25}{4} - \frac{24 + 25}{4} = 0$

${(x + \frac{5}{4})}^{2} = {(\frac{7}{4})}^{2}$

Taking square root on both sides

$x + \frac{5}{4} = \pm \frac{7}{4}$

$x = - \frac{5}{4} \pm \frac{7}{4}$

Hence,

$x = - 3, \frac{1}{2} .$

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