Answer:
x = 1 + i sqrt(7/2) or x = 1 - i sqrt(7/2)
Explanation:
Solve for x:
2 x^2 - 4 x + 9 = 0
Divide both sides by 2:
x^2 - 2 x + 9/2 = 0
Subtract 9/2 from both sides:
x^2 - 2 x = -9/2
Add 1 to both sides:
x^2 - 2 x + 1 = -7/2
Write the left hand side as a square:
(x - 1)^2 = -7/2
Take the square root of both sides:
x - 1 = i sqrt(7/2) or x - 1 = -i sqrt(7/2)
Add 1 to both sides:
x = 1 + i sqrt(7/2) or x - 1 = -i sqrt(7/2)
Add 1 to both sides:
Answer: x = 1 + i sqrt(7/2) or x = 1 - i sqrt(7/2)