Answer:
s = (i sqrt(439))/16 - 19/16 or s = -(i sqrt(439))/16 - 19/16
Explanation:
Solve for s:
1 + 3 s + 8 (s^2 + 2 s + 3) = 0
Expand out terms of the left hand side:
8 s^2 + 19 s + 25 = 0
Divide both sides by 8:
s^2 + (19 s)/8 + 25/8 = 0
Subtract 25/8 from both sides:
s^2 + (19 s)/8 = -25/8
Add 361/256 to both sides:
s^2 + (19 s)/8 + 361/256 = -439/256
Write the left hand side as a square:
(s + 19/16)^2 = -439/256
Take the square root of both sides:
s + 19/16 = (i sqrt(439))/16 or s + 19/16 = -(i sqrt(439))/16
Subtract 19/16 from both sides:
s = (i sqrt(439))/16 - 19/16 or s + 19/16 = -(i sqrt(439))/16
Subtract 19/16 from both sides:
Answer: s = (i sqrt(439))/16 - 19/16 or s = -(i sqrt(439))/16 - 19/16