Question

Solve 0 = x2 + 6x + 13 by completing the square.

A. x = 5 and x = 1
B. x = 3 + i22−−√ and x = 3 − i22−−√
C. x = −1 and x = 1
D. x = −3 + 2i and x = −3 − 2i

Answer 1

To solve the equation 0 = x² + 6x + 13 by completing the square, follow these steps: Move the constant term to the right side of the equation, take half of the coefficient of x and square it, add it to both sides of the equation, factor the left side of the equation, take the square root of both sides, and solve for x.

Step-by-step explanation:

To solve the equation 0 = x² + 6x + 13 by completing the square, follow these steps:

Start with the equation: x² + 6x + 13 = 0

Move the constant term to the right side of the equation: x² + 6x = -13

Take half of the coefficient of x, square it, and add it to both sides of the equation: x² + 6x + (6/2)² = -13 + (6/2)²

Simplify: x² + 6x + 9 = -13 + 9

Factor the left side of the equation: (x + 3)² = -4

Take the square root of both sides: x + 3 = ±√(-4)

Solve for x: x = -3 ± ±√(-4)

Therefore, the correct answer is B. x = 3 + i√22 and x = 3 - i√22.

Answer 2

x = -3 - 2i and x = -3 + 2i

Step-by-step explanation:

I was too lazy to complete the square but solved it on WolframAlpha