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[tex]|P + Vt + A(t^2)/2| = st[/tex]

where P V and A are vectors and s and t are scalars.

I've tried squaring both sides which results in the equation

[tex](|A|^2/4)t^4+V.Gt^3+(P.G+|V|^2)t^2+2P.Vt + |P|^2 = s^2t^2[/tex]

[tex](|A|^2/4)t^4+V.Gt^3+(P.G+|V|^2-s^2)t^2+2P.Vt+|P|^2=0[/tex]

The only way I can think to solve this is through the quartic formula which is too unwieldy for my purposes and was wondering if anyone had any ideas.