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

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