Question

(x – 2)^2 + 20 = 0

These are the answers I have to choose from.
a.) x = 2 + 2i , x = 2 – 2i
b.) x = –2 + 2i , x = –2 – 2i
c.) x = 2 + 2 , x = 2 – 2
d.) x = –2 + 2, x = –2 – 2

Answer 1

x = 2 ± 2 sqrt(5)i

Explanation:

(x – 2)^2 + 20 = 0

Subtract 20 from each side

(x – 2)^2 + 20 -20=0 -20

(x – 2)^2 =- 20

Take the square root of each side

sqrt((x – 2)^2) =±sqrt(- 20)

x-2 = ±sqrt(- 20)

We know sqrt(ab) = sqrt(a) sqrt(b)

x-2 = ±sqrt(- 1) sqrt(20)

We know the sqrt (-1) = i

x-2 = ±i sqrt(4*5)

x-2 = ±i sqrt(4) sqrt(5)

Add 2 to each side

x-2+2 = 2 ±i sqrt(4) sqrt(5)

x = 2 ±i 2 sqrt(5)

x = 2 ± 2 sqrt(5)i