Answer
$9$.
Work Step by Step
The function modelling the number of chess games is
$f(x)=\frac{x^2-x}{2}$
where $x$ is the number of chess players.
Plug the given value $f(x)=36$ into the function.
$36=\frac{x^2-x}{2}$
Multiply both sides by $2$ to clear fractions.
$2\cdot 36=2\cdot \left (\frac{x^2-x}{2} \right )$
Clear the parentheses and simplify.
$72=x^2-x$
Subtract $42$ from both sides.
$72-72=x^2-x-72$
Add like terms.
$0=x^2-x-72$
Write the middle term $-x$ as $-9x+8x$
$0=x^2-9x+8x-72$
Group terms.
$0=(x^2-9x)+(8x-72)$
Factor out from each term.
$0=x(x-9)+8(x-9)$
Factor out $(x-9)$
$0=(x-9)(x+8)$
Set each factor equal to zero.
$x-9=0$ or $x+8=0$
Isolate $x$.
$x=9$ or $x=-8$.
Take the positive value because the number of players cannot be negative.
Hence, the number of players who entered in the tournament $=9$.
