We are provided with a expression as follows ;
- [tex]{\sf x(27-x)=182}[/tex]
Can be further written as ;
[tex]{: \implies \quad \sf 27x-{x^{2}}=182}[/tex]
[tex]{: \implies \quad \sf {x^2} -27x + 182=0}[/tex]
Using splitting the middle term we have ;
[tex]{: \implies \quad \sf {x^2} - 13x-14x+182=0}[/tex]
[tex]{: \implies \quad \sf x(x-13)-14(x-13)=0}[/tex]
[tex]{: \implies \quad \sf (x-13)(x-14)=0}[/tex]
Case I :-
When , (x-13)=0 , then clearly x = 13
Case II :-
When , (x-14)=0 , then clearly x = 14
Hence , The required values of x are 13 and 14 respectively
