Question

The sum of a natural number and its square is $156$. Find the number.

Answer 1

Suppose the natural number $=x$

its square $x^2$

$\begin{array}{c}x+x^2=156\\ x^2+x-156=0\\ x^2+13x-12x-156=0\\ x\left(x+13\right)-12\left(x+13\right)=0\\ \left(x+13\right)\left(x-12\right)\\ x=12\\ x=-13\end{array}$

or

$x=$12