Question

Find the root of the equation 5x square-6x-2=0 by the method of compleing of the square

Answer 1

$5 {x}^{2} - 6x - 2 = 0 \\ divide \: the \: equation \: by \: 5 \: we \: get \\ {x}^{2} - \frac{6}{5} x - \frac{2}{5} = 0 \\ {x}^{2} - \frac{6}{5} x + {( \frac{6}{10}) }^{2} - { (\frac{6}{10}) }^{2} - \frac{2}{5} = 0 \\ {(x - \frac{6}{10}) }^{2} = { (\frac{6}{10}) }^{2} + \frac{2}{5} \\ {(x - \frac{3}{5}) }^{2} = \frac{9}{25} + \frac{2}{5} = \frac{9 + 10}{25} = \frac{19}{25} \\ {(x - \frac{3}{5}) }^{2} = { \frac{19}{25} } \\ x - \frac{3}{5} = \frac{ + }{ - } \sqrt{ \frac{19}{25} } \\ x = \frac{3}{5} + \sqrt{ \frac{19}{25} } \: \: or \: \: \frac{3}{5} - \sqrt{ \frac{19}{25} } \\ x = \frac{3 + \sqrt{19} }{5} \: \: or \: \: \frac{3 - \sqrt{19} }{5}$