What is the root of this equation?

2x^2 - 4x + 9 = 0

x = 1 + i sqrt (7/2) or x = 1 - i sqrt (7/2)

Step-by-step 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)