What two factors of 1080 equal the sum of 69???

I ususally use the sensible guess method too saseflower but here is another way.

What two factors of 1080 equal the sum of 69

xy=1080   (1)

x+y=69  so  y=69-x    (2)

sub 2 into 1

$$\\x(69-x)=1080\\
69x-x^2=1080\\
0=x^2-69x+1080\\
$now you can solve it with the quadratic formula$\\$$

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{69}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1\,080}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{45}}\\
{\mathtt{x}} = {\mathtt{24}}\\
\end{array} \right\}$$

Well first guess and check

I just subtracted random numbers from 69 and then multiplyed them with the difference.

I finally got 45 and 24

Basically you just have to do guess and check

x=0