Question

Quadratic equations w complex roots
x2 - 6x + 12 = 0

Answer 1

x = 3 ± i
`√(3)`

Explanation:

Given

x² - 6x + 12 = 0 ( subtract 12 from both sides )

x² - 6x = - 12

Using the method of completing the square

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

x² + 2(- 3)x + 9 = - 12 + 9

(x - 3)² = - 3 ( take the square root of both sides )

x - 3 = ±
`√(-3)` = ± i
`√(3)` ( add 3 to both sides )

x = 3 ± i
`√(3)`