Question

Solve x2 + 8x + 22 = 0 by completing the square.

Question 20 options:

A)

x = –4 + i√ 6 , x = –4 – i√ 6


B)

x = –4 + √ 14 , x = –4 – √ 14


C)

x = –4 + i√ 14 , x = –4 – i√ 14


D)

x = –4 + √ 6 , x = –4 – √ 6

Answer 1

A)

Explanation:

the solution of a squared equation is

x = (-b ± sqrt(b² - 4ac)) / (2a)

in our case

a = 1

b = 8

c = 22

x = (-8 ± sqrt(64 - 88))/2 = (-8 ± sqrt(-24))/2 =

= (-8 ± sqrt(4×-6))/2 = (-8 ± 2×sqrt(-6))/2 =

= -4 ± sqrt(-6) = -4 ± i×sqrt(6)