Which of the following is a solution of x2 - 6x = - 22?

A) negative 6 minus i square root of 52

B) negative 6 plus i square root of 13

C) 3 minus i square root of 13

D) negative 3 plus i square root of 52

C) 3 - i√13

Step-by-step explanation:

x² - 6x = - 22

x² - 6x + (-6/2) ² = - 22 + (-6/2) ²

x² - 6x + 9 = - 22 + 9

(x - 3) (x - 3) = - 13

x - 3 = ± √-13

x - 3 = ± i√13

x = 3 ± i√13

x = 3 + i√13 & x = 3 - i√13

The solution of given equation are 3±√13i.

Step-by-step explanation:

We have given a quadratic equation.

x²-6x = - 22

We have to find the solution of given equation.

We use method of completing square to solve this.

Adding (-3) ² to both sides of given equation, we have

x²-6x + (-3) ² = - 22 + (-3) ²

(x-3) ² = - 22+9

(x-3) ² = - 13

Taking square root to both sides of above equation, we have

x-3 = ±√-13

x-3 = ±√13i where i = √-1

x = 3±√13i

Hence, the solution of given equation are 3±√13i.