Roots of quadratic equation by completing the square or other method? I'm trying to find solution(s) to the following equation:
$x^2 - 5x + 3 = 0$
It seems like it can't be factored normally so I tried solving by completing the square:
$x^2-5x=-3$
$x^2-5x+6.25=-0.5$
$(x-2.5)^2 = -0.5$
That's where I get stuck since you can't get the real number square root of a negative number.
Is there another method I could use to solve this quadratic equation? Did I make a mistake?

$x^2-5x+3$ can be written as $(x-\frac 52)^2-\frac{13}4=0$ $$(x-\frac52)^2=\frac {13}4$$ $$(x-\frac52)=\pm\frac {\sqrt 13}{\sqrt 4}$$ $$(x-\frac52)=\pm\frac {\sqrt 13}{2}$$
$x= \frac {5+\sqrt13}{2}$ or $x=\frac{5-\sqrt 13}{2}$
