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 $ax^{2}+bx+c=0$.
$$-x^{2}-x+35=0$$
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 $x=\frac{1±\sqrt{141}}{-2}$ when $±$ is plus. Add $1$ to $\sqrt{141}$.
$$x=\frac{\sqrt{141}+1}{-2}$$
Divide $1+\sqrt{141}$ by $-2$.
$$x=\frac{-\sqrt{141}-1}{2}$$
Now solve the equation $x=\frac{1±\sqrt{141}}{-2}$ when $±$ is minus. Subtract $\sqrt{141}$ from $1$.
$$x=\frac{1-\sqrt{141}}{-2}$$
Divide $1-\sqrt{141}$ by $-2$.
$$x=\frac{\sqrt{141}-1}{2}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{-1-\sqrt{141}}{2}$ for $x_{1}$ and $\frac{-1+\sqrt{141}}{2}$ for $x_{2}$.
