Which of the following is a solution of x² + 6x = -22?
-6 - i√52
-6 + i√13
-3 - i√13
-3 + i√52

Solution:

Given, quadratic equation x² + 6x = -22

⇒ x² + 6x + 22 = 0

Using quadratic formula,

x = {(-b) ± √(b² - 4ac)} / 2a

Here, a = 1, b = 6 and c = 22

∴ x = {(-6) ± √(36 - 4(1)(22)} / 2(1)

x = {-6 ± √(-52)} / 2

Since the discriminant is negative, the given quadratic equation cannot be factored hence no real solution exists for the given quadratic equation.

∴ x = {-6 ± √((-1) × 52))} / 2

= {-6 ± √(i² × 4×13)} / 2

= {-6 ± 2i√13} / 2

= {2 (-3 ± i√13)} / 2

= -3 ± i√13

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

Summary:

The solution of the equation x² + 6x = -22 is -3 ± i√13. Hence third option is the correct answer.