Infinite Fractions - 8

Algebra Level 3

\(\frac { 2+\frac { 2+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } }{ { 2 }^{ 2 }+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } } }{ { 2 }^{ 2 }+\frac { 2+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } }{ { 2 }^{ 2 }+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } } } =x\)

Given that \(x\) is positive, find \(x\).

Note: Round answer to \(3\) decimal places.

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