Question

Find Roots By Completing square : 5x square - 6x - 2

Answer 1

   

$5x^2-6x-2=0 \\ \\ 5x^2-6x=2 \\ \\ x^2-\frac{6}{5}x=\frac{2}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ Divided by 5 ] \\ \\ x^2-\frac{6}{5}x+\frac{9}{25}=\frac{2}{5}+\frac{9}{25} \\ \\ (x-\frac{3}{5})^2=\frac{10}{25}+\frac{9}{25} \\ \\ (x-\frac{3}{5})^2=\frac{19}{25} \\ \\ x-\frac{3}{5}=\pm\sqrt{\frac{19}{25}} \\ \\ x-\frac{3}{5}=\pm \frac{\sqrt{19}}{5} \\ \\ x=\pm\frac{\sqrt{19}}{5}+\frac{3}{5} \\ \\ \\ x=\frac{3+\sqrt{19}}{5} \ \ \ \ \ \ \ \ \ \ \ \ OR \ \ \ \ \ \ \ \ \ \ \ \ x=\frac{3-\sqrt{19}}{5}$

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