SAT Question 30596346: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

It's given that in the equation $\frac{1}{7}(x-k)\left(16-x^2\right)=0$, $k$ is a positive constant. Multiplying both sides of this equation by $7$ yields $(x-k)\left(16-x^2\right)=0$. By the zero product property, it follows that $x-k=0$ or $16-x^2=0$. Adding $k$ to both sides of the equation $x-k=0$ yields $x=k$. Adding $x^2$ to both sides of the equation $16-x^2=0$ yields $16=x^2$. Taking the square root of both sides of this equation yields $4=x$ and $-4=x$. Therefore, the solutions to the given equation are $k$, $4$, and $-4$. It's given that the sum of the solutions to the equation is $59$. Thus, $k+4+(-4)=59$, or $k=59$.