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

Question:

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

Solution:

Let the required natural number be x.

According to the given condition,

$x+x^{2}=156$

$\Rightarrow x^{2}+x-156=0$

$\Rightarrow x^{2}+13 x-12 x-156=0$

$\Rightarrow x(x+13)-12(x+13)=0$

$\Rightarrow(x+13)(x-12)=0$

$\Rightarrow x+13=0$ or $x-12=0$

$\Rightarrow x=-13$ or $x=12$

x = 12     (x cannot be negative)

Hence, the required natural number is 12.