SAT Question a267bd29: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice D is correct. Adding $40$ to both sides of the given equation yields $w^2+12w=40$. To complete the square, adding ${\left(\frac{12}{2}\right)}^2$, or $6^2$, to both sides of this equation yields $w^2+12w+6^2=40+6^2$, or ${\left(w+6\right)}^2=76$. Taking the square root of both sides of this equation yields $w+6=\pm \sqrt{76}$, or $w+6=\pm 2\sqrt{19}$. Subtracting $6$ from both sides of this equation yields $w=-6\pm 2\sqrt{19}$. Therefore, the solutions to the given equation are $-6+2\sqrt{19}$ and $-6-2\sqrt{19}$. Of these two solutions, only $-6+2\sqrt{19}$ is given as a choice.