Solve x^2-4x+5=0 by completing the square

x = 2 ± i

Step-by-step explanation:

1. Identify the coefficient of x. Here that coefficient is - 4.

2. Take half of this coefficient, obtaining - 2.

3. Square this result, obtaining 4

4. Now add 4 to both sides of the given equation:

x^2 - 4x + 4 + 5 = 4

5. Rewrite the perfect square x^2 - 4x + 4 as the binomial (x - 2) ^2:

(x - 2) ^2 = - 1

6. Take the square root of both sides:

x - 2 = ±√ (-1) = ±i

7. Solve for x: x = 2 ±i