To solve the inequality, factor the left hand side. Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$x^{2}-5x+2=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. Substitute $1$ for $a$, $-5$ for $b$, and $2$ for $c$ in the quadratic formula.
For the product to be $≥0$, $x-\frac{\sqrt{17}+5}{2}$ and $x-\frac{5-\sqrt{17}}{2}$ have to be both $≤0$ or both $≥0$. Consider the case when $x-\frac{\sqrt{17}+5}{2}$ and $x-\frac{5-\sqrt{17}}{2}$ are both $≤0$.
