OpenSAT

A quadratic equation has exactly one solution when its discriminant is equal to zero. The discriminant of the quadratic equation $ax^2 + bx + c = 0$ is $b^2 - 4ac$. For the given equation, $a = 1$, $b = -2$, and $c = k$. Setting the discriminant equal to zero, we get $(-2)^2 - 4(1)(k) = 0$, or $4 - 4k = 0$. Solving for $k$ yields $k = 1$.