\(350-2\times\left(2\times x-1\right)^3=10^2\)
\(350-2\times\left(2\times x-1\right)^3=100\)
\(2\times\left(2\times x-1\right)^3=350-100\)
\(2\times\left(2\times x-1\right)^3=250\)
\(\left(2\times x-1\right)^3=250:2\)
\(\left(2\times x-1\right)^3=125\)
\(\left(2\times x-1\right)^3=5^3\)
\(2\times x-1=5\)
\(2\times x=5+1\)
\(2\times x=6\)
\(x=6:2\)
\(\Rightarrow x=3\)