x + 4x = 4 => 5x = 4 => x = 4/5.

In real arithmetic, negative numbers do not have real square roots (in complex numbers, √(-25) = 5i), so 'None of these' is the correct option.

'Lionize' means to treat someone with great public acclaim or celebrity status; its opposite is 'Vilify' (to disparage or defame publicly).

A 'Solipsist' holds that only the self exists or matters (extreme self-absorption); its direct opposite character trait is 'Selfless'.

'Mélange' refers to a varied mixture or medley of different elements; its antonym is 'Homogeneous' (uniform throughout).

'Egregious' means conspicuously bad or shockingly offensive; its antonym is 'Inconspicuous' (unnoticeable or subtle).

A 'Bastion' is a strongly fortified stronghold or defensive structure; its direct conceptual antonym is 'Defenseless'.

'Verisimilitude' is the appearance or semblance of truth or reality in art and literature, synonymous with 'Realism'.

'Metanoia' is a theological and psychological term denoting a transformative change of heart, spiritual conversion, or 'Repentance'.

A 'Sobriquet' is a familiar name or descriptive epithet given to a person or place, meaning 'Nickname'.