Answer
$\color{blue}{\left\{2, 5\right\}}$
Work Step by Step
The solutions of the quadratic equation $ax^2+bx+c=0$ can be found using the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
The given quadratic equation has $a=1, b=-7, \text{ and } c= 10$.
Substitute these values into the quadratic formula to obtain:
\begin{align*}
x&=\frac{-(-7)\pm\sqrt{(-7)^2-4(1)(10)}}{2(1)}\\\\
x&=\frac{7\pm \sqrt{49-40}}{2}\\\\
x&=\frac{7\pm \sqrt{9}}{2}\\\\
x&=\frac{7\pm 3}{2}\\\\
\end{align*}
Thus,
$x_1=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\$
$x_2=\dfrac{7+3}{2}=\dfrac{10}{2}=5$
Therefore, the solution set is $\color{blue}{\left\{2, 5\right\}}$.
