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 $ax^{2}+bx+c=0$.
$$x^{2}+18x+49=0$$
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.
$$x=\frac{-18±\sqrt{18^{2}-4\times 49}}{2}$$
Square $18$.
$$x=\frac{-18±\sqrt{324-4\times 49}}{2}$$
Multiply $-4$ times $49$.
$$x=\frac{-18±\sqrt{324-196}}{2}$$
Add $324$ to $-196$.
$$x=\frac{-18±\sqrt{128}}{2}$$
Take the square root of $128$.
$$x=\frac{-18±8\sqrt{2}}{2}$$
Now solve the equation $x=\frac{-18±8\sqrt{2}}{2}$ when $±$ is plus. Add $-18$ to $8\sqrt{2}$.
$$x=\frac{8\sqrt{2}-18}{2}$$
Divide $-18+8\sqrt{2}$ by $2$.
$$x=4\sqrt{2}-9$$
Now solve the equation $x=\frac{-18±8\sqrt{2}}{2}$ when $±$ is minus. Subtract $8\sqrt{2}$ from $-18$.
$$x=\frac{-8\sqrt{2}-18}{2}$$
Divide $-18-8\sqrt{2}$ by $2$.
$$x=-4\sqrt{2}-9$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-9+4\sqrt{2}$ for $x_{1}$ and $-9-4\sqrt{2}$ for $x_{2}$.
