Question

Solve the equations by completing the square
$x^2-5x+5=0$

Answer 1

$x^2-5x+5=0$

Or, $x^2-2.\frac{5}{2}x+{\left(\frac{5}{2}\right)}^2-{\left(\frac{5}{2}\right)}^2+5=0$

Or$,{(x-\frac{5}{2})}^2+5-\frac{25}{4}=0$

Or,${(x-\frac{5}{2})}^2-{\left(\frac{\sqrt{5}}{2}\right)}^2=0$

Or, $(x-\frac{5}{2}+\frac{\sqrt{5}}{2})(x-\frac{5}{2}-\frac{\sqrt{5}}{2})=0$

$\therefore x=\frac{5-\sqrt{5}}{2}$ or $x=\frac{5+\sqrt{5}}{2}$