Question

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

Answer 1

C) 3 - i√13

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

Answer 2

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

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.