Question

Solve x2 + 4x + 12 = 0 by completing the square.
(options in attachment)

Answer 1

second option

Explanation:

x² + 4x + 12 = 0 ( subtract 12 from both sides )

x² + 4x = - 12

to complete the square

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

x² + 2(2)x + 4 = - 12 + 4

(x + 2)² = - 8 ( take square root of both sides )

x + 2 = ±
`√(-8)` = ±
`√(4(2)(-1))` = ± (
`√(4)` ×
`√(2)` ×
`√(-1)` ) = ± 2
`√(2)` i

subtract 2 from both sides

x = - 2 ± 2
`√(2)` i

then

x = - 2 + 2
`√(2)` i , x = - 2 - 2
`√(2)` i