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 $ax^{2}+bx+c=0$.
$$-576x^{2}-18x+301=0$$
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 $x=\frac{18±6\sqrt{19273}}{-1152}$ when $±$ is plus. Add $18$ to $6\sqrt{19273}$.
$$x=\frac{6\sqrt{19273}+18}{-1152}$$
Divide $18+6\sqrt{19273}$ by $-1152$.
$$x=-\frac{\sqrt{19273}}{192}-\frac{1}{64}$$
Now solve the equation $x=\frac{18±6\sqrt{19273}}{-1152}$ when $±$ is minus. Subtract $6\sqrt{19273}$ from $18$.
$$x=\frac{18-6\sqrt{19273}}{-1152}$$
Divide $18-6\sqrt{19273}$ by $-1152$.
$$x=\frac{\sqrt{19273}}{192}-\frac{1}{64}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $-\frac{1}{64}-\frac{\sqrt{19273}}{192}$ for $x_{1}$ and $-\frac{1}{64}+\frac{\sqrt{19273}}{192}$ for $x_{2}$.
