If $x=2$cos36°, then $x$ satisfies which equation?

cos36° = (√5 + 1)/4, so $x$ = (√5 + 1)/2 ≈ 1.618 — the golden ratio. Then $x^2$ = (6 + 2√5)/4 = (3 + √5)/2, which is exactly $x+1$, so $x^2-x-1=0$. Numerically $1.618^2=2.618=1.618+1$. The companion value 2cos72° ≈ 0.618 is the positive root of $x^2+x-1=0$, while $x^2-x+1=0$ has no real root at all.