roots of a quadratic

Yeah idk what you mean because x=((-2+3sqrt2)/2)^2+((-2-3sqrt2)/2)^2 is not funky

It's around -8.5, but you figure it out.

Yay!

2x^2  + 4x  - 1   =  6     rearrange   as

2x^2  + 4x - 7  =  0         

Call the solutions   a, b

The sum of  these  solutions   =  -4/2  =  -2 =  a + b

The product of these solutions  =   -7/2 =  ab    ⇒    2ab  =   -7       (1)

So

a + b =  -2

Square both sides

a^2  + 2ab  + b^2  =  4     (2)

Sub (1)  into (2)

a^2   - 7  + b^2  = 4            add 7 to both sides

a^2  + b^2   =    11