It is given that \(x\) satisfies the equation \(3 ^ { 2 x } = 5 \left( 3 ^ { x } \right) + 14\). Find the value of \(3 ^ { x }\) and, using logarithms, find the value of \(x\) correct to 3 significant figures.
Hence state the values of \(x\) satisfying the equation \(3 ^ { 2 | x | } = 5 \left( 3 ^ { | x | } \right) + 14\).