Question

What are the solutions to

x^2+4x+4=12

A. x=2√3+2
B. x=2√3-2
C=-√2+12
D=√2+12
E=-2√3+2
F=-2√3-2​

Answer 1

B and F

Explanation:

Given

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

x² + 4x = 8

Using the method of completing the square to solve for x

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

x² + 2(2)x + 4 = 8 + 4, that is

(x + 2)² = 12 ( take the square root of both sides )

x + 2 = ±
`√(12)` ( subtract 2 from both sides )

x = ±
`√(12)` - 2

= ± 2
`√(3)` - 2

Hence

x = 2
`√(3)` - 2 → B

x = - 2
`√(3)` - 2 → F