Question

How do you solve `2x^2-2x+7=5` by completing the square?

Answer 1

`x = (1 +- isqrt3)/2`

Explanation:

`2x^2 - 2x = - 2`
`x^2 - x = - 1`
`x^2 - x + 1/4 = - 1 + 1/4`
`(x - 1/2)^2 = - 3/4 = (3i^2)/4`
There are 2 complex roots:
`x - 1/2 = +- (isqrt3)/2`
`x = 1/2 +- (isqrt3)/2 = (1 +- isqrt3)/2`