SAT Question 88a0c425: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice B is correct. It's given that the equation $-2x^2+20x+c=0$, where $c$ is a constant, has exactly one solution. A quadratic equation of the form $a{x}^2+bx+c=0$ has exactly one solution if and only if its discriminant, $b^2-4ac$, is equal to zero. It follows that for the given equation, $a=-2$ and $b=20$. Substituting $-2$ for $a$ and $20$ for $b$ in $b^2-4ac$ yields $20^2-4(-2)(c)$, or $400+8c$. Since the discriminant must equal zero, it follows that $400+8c=0$. Subtracting $400$ from both sides of this equation yields $8c=-400$. Dividing each side of this equation by $8$ yields $c=-50$. Therefore, the value of $c$ is $-50$.