Can you find the roots of x^2 -4x +5? or help me with quadratic equations?

Question

I can get some quadratic equations, but i do them a long way. please can you show me how to do it a quick way.

Answer 1

Quickest way here, since the x² has a (one) in front and the -4 is even, is to complete the square:

x² - 4x + 5 = 0
x² - 4x + 4 = -5 + 4
(x - 2)² = -1
x - 2 = ±√-1 = ±i
x = 2 ± i

Answer 2

Aply x = [-b +/- sqrt (b^2 - 4ac)] / 2a

x = [4 +/- sqrt (16 - 20)] / 2

x = 2 +/- i

where i = sqrt (-1)