Answer:
u = 3/8 + sqrt(73)/8 or u = 3/8 - sqrt(73)/8
Step-by-step explanation:
Solve for u over the real numbers:
-8 u^2 + 6 u + 8 = 0
Divide both sides by -8:
u^2 - (3 u)/4 - 1 = 0
Add 1 to both sides:
u^2 - (3 u)/4 = 1
Add 9/64 to both sides:
u^2 - (3 u)/4 + 9/64 = 73/64
Write the left hand side as a square:
(u - 3/8)^2 = 73/64
Take the square root of both sides:
u - 3/8 = sqrt(73)/8 or u - 3/8 = -sqrt(73)/8
Add 3/8 to both sides:
u = 3/8 + sqrt(73)/8 or u - 3/8 = -sqrt(73)/8
Add 3/8 to both sides:
Answer: u = 3/8 + sqrt(73)/8 or u = 3/8 - sqrt(73)/8
