Question

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

Answer 1

This question doesn't have any real solutions. However it does have two complex solutions;
`color(red)(x=(1+-isqrt(39))/4)`

Explanation:

`2x^2-x=-5`
`2x^2-x+5=0`
`2(x^2-x/2+5/2)=0`
`x^2-x/2+5/2=0`
`(x-1/4)^2-1/16+5/2=0`
`(x-1/4)^2+39/16=0`
`(x-1/4)^2=-39/16`
`x-1/4=+-sqrt(-39/16)`
`x-1/4=+-sqrt(-39)/4=+-(sqrt(39)xxsqrt(-1))/4`
`x=1/4+-(sqrt(39)xxsqrt(-1))/4=1/4+-(sqrt(39)xxi)/4`
`color(red)(x=(1+-isqrt(39))/4)`

I hope it helps :)