Find the complex factors of the quadratic trinomial x^2+8x+17

[x+(4-i)][x+(4+i)]

Step-by-step explanation:

Complete the square then regroup the first two terms. Add and subtract: (b/2)^2=(8/2)^2=16

x^2+8x+17=(x^2+8x)+17

=(x^2+8x+16)+17-16

=(x+4)^2+1  create a difference of squares using i^2= -1

=(x+4)^2 - (-1)

=(x+4)^2 - i^2  use the difference of two squares identity

=[(x+4) - i][(x+4)+i]

=[x+(4-i)][x+(4+i)]

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x