Question

How do you use the sum of two squares formula to solve `4x^2 -8=0`?

Answer 1

I am not sure that this is what you want, but...
Considering: `(a^2-b^2)=(a+b)(a-b)`
Write:
`4x^2-8=0`
As:
`(2x+sqrt(8))(2x-sqrt(8))=0`

So:
`(2x+sqrt(8))=0`
`(2x-sqrt(8))=0`
`x_1=-sqrt(8)/2`
`x_2=sqrt(8)/2`