Question

What are the solutions of 3x2 + 6x + 6 = 0?

A. −2 ± i
B. −2 ± 2i
C. −1 ± i
D. 1 ± i

Answer 1

C

Explanation:

3x² + 6x + 6 = 0 ( divide through by 3 )

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

x² + 2x = - 2

Using 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 square root of both sides )

x + 1 = ±
`√(-1)` = ± i ( subtract 1 from both sides )

x = - 1 ± i → C