SAT Question f65288e8: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

Choice A is correct. The given equation can be rewritten as $\frac{1}{(x+5{)}^2}=4$. Multiplying both sides of this equation by $(x+5{)}^2$ yields $1=4\times (x+5{)}^2$. Dividing both sides of this equation by $4$ yields $\frac{1}{4}=(x+5{)}^2$. Taking the square root of both sides of this equation yields $\frac{1}{2}=x+5$ or $-\frac{1}{2}=x+5$. Therefore, a possible value of $x+5$ is $\frac{1}{2}$.