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 $ax^{2}+bx+c=0$.
$$x^{2}+15x+15=0$$
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.
$$x=\frac{-15±\sqrt{15^{2}-4\times 15}}{2}$$
Square $15$.
$$x=\frac{-15±\sqrt{225-4\times 15}}{2}$$
Multiply $-4$ times $15$.
$$x=\frac{-15±\sqrt{225-60}}{2}$$
Add $225$ to $-60$.
$$x=\frac{-15±\sqrt{165}}{2}$$
Now solve the equation $x=\frac{-15±\sqrt{165}}{2}$ when $±$ is plus. Add $-15$ to $\sqrt{165}$.
$$x=\frac{\sqrt{165}-15}{2}$$
Now solve the equation $x=\frac{-15±\sqrt{165}}{2}$ when $±$ is minus. Subtract $\sqrt{165}$ from $-15$.
$$x=\frac{-\sqrt{165}-15}{2}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-15+\sqrt{165}}{2}$ for $x_{1}$ and $\frac{-15-\sqrt{165}}{2}$ for $x_{2}$.
