Question 170893
solve this quadratic equation by completing the square. 
a^2 - 4a + 5 = 0
---
a^2 - 4a + ? = -5 + ?

a^2 -4a + (-4/2)^2 = -5 + (-4/2)^2

a^2 - 4a + 4 = -5 + 4

a^2 - 4a + 4 = -1

(a-2)^2 = -1

a-2 = i or a-2 = -i

a = 2+i or a = 2-i
======================
Comment: If you have not studied complex numbers the 
answer you would get would be "no solution".
======================
Cheers,
Stan H.