Question

What are the solutions of x^2 - 2x +2 = 0?

A. X= i Or x= -i
OB. X= 2+ i or x = 2- I
O C. x = 1+i or x = 1-i
O D. x = 2i or x = -2i

Answer 1

C

Explanation:

Given

x² - 2x + 2 = 0 ( subtract 2 from both sides )

x² - 2x = - 2

To solve use the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 1)x + 1 = - 2 + 1

(x - 1)² = - 1 ( take the square root of both sides )

x - 1 = ±
`√(-1)` = ± i ( add 1 to both sides )

x = 1 ± i , then

x = 1 + i or x = 1 - i → C