sqrt(2*sqrt(2 - t)) = 7 - t
\(\sqrt{2*\sqrt{2 - t}} = 7 - t\\ 2*\sqrt{2 - t} = t^2-14t+49\\ \sqrt{2 - t} =\frac{ t^2-14t+49}{2}\\ 2 - t =\frac{( t^2-14t+49)( t^2-14t+49)}{4}\\ 8 - 4t =( t^2-14t+49)( t^2-14t+49)\\ 0 =( t^2-14t+49)( t^2-14t+49)+4t-8 \)
\(0=2401 - 1372 t + 294 t^2 - 28 t^3 + t^4+4t-8\\ 0=t^4 - 28 t^3 + 294 t^2 - 1368 t + 2393\)
Wolfram alpha says no real solutions.
You do need to check my algebra though. (for careless errors)
LaTex:
\sqrt{2*\sqrt{2 - t}} = 7 - t\\
2*\sqrt{2 - t} = t^2-14t+49\\
\sqrt{2 - t} =\frac{ t^2-14t+49}{2}\\
2 - t =\frac{( t^2-14t+49)( t^2-14t+49)}{4}\\
8 - 4t =( t^2-14t+49)( t^2-14t+49)\\
0 =( t^2-14t+49)( t^2-14t+49)+4t-8