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 $ax^{2}+bx+c=0$.
$$14x^{2}-42x-70=0$$
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 $x=\frac{42±14\sqrt{29}}{28}$ when $±$ is plus. Add $42$ to $14\sqrt{29}$.
$$x=\frac{14\sqrt{29}+42}{28}$$
Divide $42+14\sqrt{29}$ by $28$.
$$x=\frac{\sqrt{29}+3}{2}$$
Now solve the equation $x=\frac{42±14\sqrt{29}}{28}$ when $±$ is minus. Subtract $14\sqrt{29}$ from $42$.
$$x=\frac{42-14\sqrt{29}}{28}$$
Divide $42-14\sqrt{29}$ by $28$.
$$x=\frac{3-\sqrt{29}}{2}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{3+\sqrt{29}}{2}$ for $x_{1}$ and $\frac{3-\sqrt{29}}{2}$ for $x_{2}$.
