Question

Find the roots of the equation 5 x square - 6 x minus 2 equals to zero by the method of completing square method

Answer 1

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Answer 2

Given,

$5 {x}^{2} - 6x - 2 = 0$

Now we follow the Algorithm.

Dividing both sides by 5.

${x}^{2} - \frac{6}{5}x - \frac{2}{5} = 0$

${x}^{2} - \frac{6}{5} x = \frac{2}{5}$

Adding (3/5)^2 on both sides

${x}^{2} - \frac{6}{5} x + {( \frac{3}{5}) }^{2} = \frac{2}{5} + { \frac{3}{5} }^{2}$

${(x - \frac{3}{5}) }^{2} = \frac{19}{25}$

$x - \frac{3}{5} = ± \: \sqrt{ \frac{19}{25} }$

$x = \frac{3}{5} + \frac{ \sqrt{19}}{5} \: or \: x = \frac{3}{5} - \frac{ \sqrt{19} }{5}$

$x = \frac{3 + \sqrt{19} }{5} \: or \: x = \frac{3 - \sqrt{19} }{5}$

$\huge \: Therefore \: the \: roots \: of \: the \: equation \: are \: \frac{3 + \sqrt{19} }{5} and \: \frac{3 - \sqrt{19} }{5}.$