Which of the following is a solution of x² + 2x = -2?
(x + (-i + 1)),  (x - (-i + 1)), (x - (-i - 1)), (x + (-i - 1))

Solution:

Given equation x² + 2x = -2

⇒ x² + 2x + 2 = 0

The given equation i.e. x² + 2x + 2 is a quadratic equation of the form ax² + bx + c

Here a = 1, b = 2, c = 2

b² - 4ac = 2² - 4 ×1 × 2 = 4 - 8 = -4

The roots of the equation are as follows:

The roots of the quadratic equation ax² +bx + c are:

(1) (-b/2a) + (√b² - 4ac)/2a = [-2/(2 × 1)] + (√2² - 4 × 1 × 2)/(2 × 6) = (-1) + √-4/2 = -1 + i

(2) (-b/2a) - (√b² - 4ac)/2a = [-2/(2 × 1)] - (√2² - 4 × 1 × 2)/(2 × 6) = (-1/6) - √-4/2 = -1 - i

The two factors of the equation are: (x - (i - 1)) and (x - (-i - 1))

Hence from the given options,(x - (-i - 1)) is the solution.

Which of the following is a solution of x² + 2x = -2?

Summary:

Factoring x² + 2x +2 we get the factors (x - (i -1)) and (x - (-i -1)).Hence from the given options,(x - (-i - 1)) is the solution.