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 $ax^{2}+bx+c=0$.
$$x^{2}-6x-20=0$$
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 $x=\frac{6±2\sqrt{29}}{2}$ when $±$ is plus. Add $6$ to $2\sqrt{29}$.
$$x=\frac{2\sqrt{29}+6}{2}$$
Divide $6+2\sqrt{29}$ by $2$.
$$x=\sqrt{29}+3$$
Now solve the equation $x=\frac{6±2\sqrt{29}}{2}$ when $±$ is minus. Subtract $2\sqrt{29}$ from $6$.
$$x=\frac{6-2\sqrt{29}}{2}$$
Divide $6-2\sqrt{29}$ by $2$.
$$x=3-\sqrt{29}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $3+\sqrt{29}$ for $x_{1}$ and $3-\sqrt{29}$ for $x_{2}$.
