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?

$(x-2.5)^2+3-2.5^2=0$
$x=(2.5)+(3.25)^{1/2}$
$x=(2.5)-(3.25)^{1/2}$
Also, since you're asking for another method, try the quadratic formula. 
$x = \frac{-b\pm \sqrt{b^{2} - 4 ac}}{2a}$
where $a, b, c$ are the coefficients of $ax^2+bx+c=0$
