SAT Question 041eda89: Nonlinear Equations In One Variable And Systems Of Equations In Two Variables answer and explanation with Desmos solution

The solutions to a quadratic equation in the form $a{x}^2+bx+c=0$, where $a$, $b$, and $c$ are constants, can be calculated using the quadratic formula, which gives two solutions: $x=\frac{-b+\sqrt{b^2-4ac}}{2a}$ and $x=\frac{-b-\sqrt{b^2-4ac}}{2a}$. The given equation is in the form $a{x}^2+bx+c=0$, where $a=1$, $b=7$, and $c=5$. It follows that one solution to the given quadratic equation is $x=\frac{-7+\sqrt{7^2-4(1)(5)}}{2(1)}$, or $x=\frac{-7+\sqrt{49-20}}{2}$, which is equivalent to $x=\frac{-7+\sqrt{29}}{2}$. It's given that one solution to the given equation can be written as $x=\frac{-7+\sqrt{k}}{2}$, where $k$ is a constant. It follows that the value of $k$ is $29$.