Answer:
t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32
Explanation:
Solve for t:
16 t^2 - 23 t + 18 = 0
Divide both sides by 16:
t^2 - (23 t)/16 + 9/8 = 0
Subtract 9/8 from both sides:
t^2 - (23 t)/16 = -9/8
Add 529/1024 to both sides:
t^2 - (23 t)/16 + 529/1024 = -623/1024
Write the left hand side as a square:
(t - 23/32)^2 = -623/1024
Take the square root of both sides:
t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32
Add 23/32 to both sides:
t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32
Add 23/32 to both sides:
Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32