Answer
The provided statement does not make sense.
Work Step by Step
The equation is ${{x}^{2}}+x+1$.
Here, the middle term cannot be expressed as the sum of two monomials and the product of monomials cannot be expressed in product of constant and first term.
So, the factorization technique becomes complicated and we will search for the quadratic expression formulae as:
$x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
where $a=1,b=1\text{ and }c=1$ so:
$\begin{align}
& x=\frac{-1\pm \sqrt{{{\left( 1 \right)}^{2}}-4\times 1\times 1}}{2\times 1} \\
& x=\frac{-1+\sqrt{-3}}{2},\frac{-1-\sqrt{-3}}{2}
\end{align}$
