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 $ax^{2}+bx+c=0$.
$$7m^{2}-7m-8=0$$
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 $m=\frac{7±\sqrt{273}}{14}$ when $±$ is plus. Add $7$ to $\sqrt{273}$.
$$m=\frac{\sqrt{273}+7}{14}$$
Divide $7+\sqrt{273}$ by $14$.
$$m=\frac{\sqrt{273}}{14}+\frac{1}{2}$$
Now solve the equation $m=\frac{7±\sqrt{273}}{14}$ when $±$ is minus. Subtract $\sqrt{273}$ from $7$.
$$m=\frac{7-\sqrt{273}}{14}$$
Divide $7-\sqrt{273}$ by $14$.
$$m=-\frac{\sqrt{273}}{14}+\frac{1}{2}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{1}{2}+\frac{\sqrt{273}}{14}$ for $x_{1}$ and $\frac{1}{2}-\frac{\sqrt{273}}{14}$ for $x_{2}$.
