Question

1. Solve. (Find all complex-number solutions.)

x2 + 4x + 6 = 0

2. Solve by factoring:

x2 + 5x = −6

PLEASE SOLVE BOTH & WRITE STEPS IN DETAIL ON YOU SOLVED IT!

Answer 1

1)
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 4
c = 6

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = -8

roots:
x = -4+sqrt(-8) / 2
= -4+isqrt(8)/2
= -4 + 2isqrt(2)/2
= -2 + i sqrt(2)

x = -4-sqrt(-8) / 2
= -4 - isqrt(8)/2
= -4 - 2isqrt(2)/2
= -2 - i sqrt(2)

Answer:
-2 - i sqrt(2)
-2 + i sqrt(2)

2)
x^2 + 5x = -6
x^2 + 5x + 6 = 0
x^2 + 3x + 2x + 6 = 0
x (x+3) + 2(x+3) = 0
(x+3)(x+2) = 0
x = -3 and x=-2

Answer:
-3
-2