Question

Find the roots by completing the square 1 )5x^2-6x-2

Answer 1

$5 {x}^{2} - 6x - 2 = 0 \\ {x}^{2} - \frac{6}{5} x - \frac{2}{5} = 0 \\ {x}^{2} - \frac{6}{5} x + \frac{9}{25} - \frac{9}{25} - \frac{2}{5} = 0 \\ {x}^{2} - \frac{6}{5} x + \frac{9}{25} - \frac{ 19}{25} = 0 \\ {(x - \frac{3}{5} )}^{2} - \frac{19}{25} = 0 \\ x - \frac{3}{5} = + \: \: or \: \: - \frac{ \sqrt{19} }{5} \\ x = \frac{3 + \sqrt{19} }{5} \: \: or \: \: \frac{3 - \sqrt{19} }{5}$