Question

Which of the following is a solution of x2 + 2x + 8? (1 point)

4 + i times the square root of 7

−1 + i times the square root of 7

1 + i times the square root of 7

−4 + i times the square root of 7

Answer 1

−1 + i times the square root of 7

Step-by-step explanation

x² + 2x + 8

I will use the complete square method to find the value of x.

x² + 2x + 8

x² + 2x = -8

x² + 2x + (2/2)² = -8 + (2/2)²

x² + 2x + 1 = -7

(x + 1)² = -7

x + 1 = √(-7)

x = √(-7) - 1

= i√7 - 1

= -1 + i√7

−1 + i times the square root of 7