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 $ax^{2}+bx+c=0$.
$$5x^{2}+40x+16=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
Now solve the equation $x=\frac{-40±16\sqrt{5}}{10}$ when $±$ is plus. Add $-40$ to $16\sqrt{5}$.
$$x=\frac{16\sqrt{5}-40}{10}$$
Divide $-40+16\sqrt{5}$ by $10$.
$$x=\frac{8\sqrt{5}}{5}-4$$
Now solve the equation $x=\frac{-40±16\sqrt{5}}{10}$ when $±$ is minus. Subtract $16\sqrt{5}$ from $-40$.
$$x=\frac{-16\sqrt{5}-40}{10}$$
Divide $-40-16\sqrt{5}$ by $10$.
$$x=-\frac{8\sqrt{5}}{5}-4$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-4+\frac{8\sqrt{5}}{5}$ for $x_{1}$ and $-4-\frac{8\sqrt{5}}{5}$ for $x_{2}$.
