SAT Question ff2e5c76: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. Adding $10$ to each side of the given equation yields $x^2-40x=10$. To complete the square, adding ${\left(\frac{40}{2}\right)}^2$, or $20^2$, to each side of this equation yields $x^2-40x+20^2=10+20^2$, or ${\left(x-20\right)}^2=410$. Taking the square root of each side of this equation yields $x-20=\pm \sqrt{410}$. Adding $20$ to each side of this equation yields $x=20\pm \sqrt{410}$. Therefore, the solutions to the given equation are $x=20+\sqrt{410}$ and $x=20-\sqrt{410}$. The sum of these solutions is $\left(20+\sqrt{410}\right)+\left(20-\sqrt{410}\right)$, or $40$.