Test each option in $x + x^2 = 1$:

• $x = -1$: $(-1) + (-1)^2 = -1 + 1 = 0 \neq 1$
• $x = 0$: $0 + 0 = 0 \neq 1$
• $x = \dfrac{1}{2}$: $\dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} \neq 1$
• $x = 1$: $1 + 1 = 2 \neq 1$

Solving $x^2 + x - 1 = 0$: $x = \dfrac{-1 \pm \sqrt{5}}{2}$, which gives irrational values not among the standard choices. Therefore, none of the listed options is a solution.