Question

5x^2-4x-3=0 by completing square method​

Answer 1

$5 {x}^{2} - 4x - 3 = 0 \\ \frac{5 {x}^{2} }{5} - \frac{4x}{5} - \frac{3}{5} = 0 \\ {x}^{2} - \frac{4x}{5} - \frac{3}{5} = 0 \\ {x}^{2} - (2)(x)( \frac{2}{5} ) + {( \frac{2}{5}) }^{2} - \frac{3}{5} = 0 + { (\frac{2}{5}) }^{2} \\ {(x - \frac{2}{5}) }^{2} - \frac{3}{5} = 0 + \frac{4}{25} \\ {(x - \frac{2}{5} )}^{2} = \frac{4}{25} + \frac{3}{5} \\ {(x - \frac{2}{5} )}^{2} = \frac{4 + 15}{25} \\ {(x - \frac{2}{5} )}^{2} = \frac{19}{25} \\ x - \frac{2}{5} = ±\sqrt{ \frac{19}{25} } \\ x - \frac{2}{5} = ±\frac{ \sqrt{19} }{5} \\ x = \frac{ \sqrt{19} }{5} + \frac{2}{5} = \frac{2 + \sqrt{19} }{5} \: or \\ \: x = - \frac{ \sqrt{19} }{5} + \frac{2}{5} \\ x = \frac{2 - \sqrt{19} }{5}$