The roots of `7x^2+1=-140` have to be determined.

`7x^2+1=-140`

=> `7x^2=-140-1`

=> `x^2 = -141/7`

The roots are `x1 = sqrt(141/7)*i` and `x2 = -sqrt(141/7)*i`

Substituting the roots in the original equation:

- `7*(sqrt(141/7)*i)^2 + 1`

= `7*(-141/7) + 1`

= -141 + 1

= -140

- `7*(-sqrt(141/7)*i)^2 + 1`

= `7*(-141/7)...

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The roots of `7x^2+1=-140` have to be determined.

`7x^2+1=-140`

=> `7x^2=-140-1`

=> `x^2 = -141/7`

The roots are `x1 = sqrt(141/7)*i` and `x2 = -sqrt(141/7)*i`

Substituting the roots in the original equation:

- `7*(sqrt(141/7)*i)^2 + 1`

= `7*(-141/7) + 1`

= -141 + 1

= -140

- `7*(-sqrt(141/7)*i)^2 + 1`

= `7*(-141/7) + 1`

= -141 + 1

= -140

**This proves that the roots of the equation are **` +-sqrt(141/7)*i`