9514 1404 393
Answer:
-5/4 +i(√2)/4 and -5/4 -i(√2)/4
Step-by-step explanation:
I find simplest form to be easier to get to if the leading coefficient is 1. Dividing by 16, we have ...
x^2 +5/2x +27/16 = 0
Completing the square by adding and subtracting the square of half the x-coefficient, we get ...
(x^2 +5/2x +25/16) +27/16 -25/16 = 0
(x +5/4)^2 = 2/16
Subtracting 2/16, taking the square root, and subtracting 5/4 gives ...
x +5/4 = ±√(-2/16)
x = -5/4 ±i(√2)/4
The roots are -5/4 +i(√2)/4 and -5/4 -i(√2)/4.
