Imaginary Equations (Problem 1, Version 2)

$\begin{aligned} i^2 + x &= \sqrt{2} + \phi \\ x-1 &= \sqrt{2} + \frac{1 + \sqrt{5}}{2} \\ x &= \sqrt{2} + \frac{1 + \sqrt{5}+2}{2} \\ x &\approx \boxed{4.032} \end{aligned}$

$i^2 = -1$ so $-1 + x$ = $√2 + \phi$ . $√2 + \phi$ = $3.03224755112$ so $-1 + x = 3.03224755112$ so $x = 4.03224755112 = 4.032$