Numerical Methods: Euler to Runge–Kutta · Hard problem

Apply one step of the backward Euler method $y_1 = y_0 + h\,f(t_1, y_1)$ with $h = \dfrac{1}{2}$ to $y' = -y^2$, $y(0) = 1$. The implicit equation has two roots; take the one near $y_0$ (the positive one). What is $y_1$?