Question

5. What are the solutions of the equations x2 - 4x = -5

a. 2 + 2i
b. 2 - i
c. 2 + i.
d. 2 - 2 i

Answer 1

b and c

Explanation:

Given

x² - 4x = - 5

Solve by using the method of completing the square

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

x² + 2(- 2)x + 4 = - 5 + 4

(x - 2)² = - 1 ( take the square root of both sides )

x - 2 = ±
`√(-1)` = ± i ( add 2 to both sides )

x = 2 ± i

Then solutions are

x = 2 - i → b

x = 2 + i → c