Question

How can solve by completing square method $x^2-5x+5=0$

Answer 1

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

$x^2-5x=-5$

(1) Divide the equation by the coefficient of $x^2$

$x^2-\frac{5}{1}x=-\frac{5}{1}$

(2) Add the square of half the coefficient of $x$ , both sides

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

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

$\Rightarrow x-\frac{5}{2}=\pm \sqrt{\frac{5}{4}}=\pm \frac{\sqrt{5}}{2}$

$x=\frac{5}{2}\pm \frac{\sqrt{5}}{2}$