Answer
$x=2$ and $x=9$
Work Step by Step
We are given that $18=11x-x^{2}$. We can first subtract 18 from both sides of the equation to get all terms on one side.
$-x^{2}+11x-18=0$
Next, we can multiply each term on both sides by -1 so the term $x^{2}$ will have a positive coefficient.
$x^{2}-11x+18=0$
We know that 2 and 9 are factors of 18 and the sum of -2 and -9 is equal to $-2+(-9)=-11$ (which is the coefficient attached to the middle term). Therefore, we can factor the existing polynomial into $(x-2)(x-9)=0$
Set both terms in parentheses equal to 0.
$x-2=0$
Add 2 to both sides.
$x=2$
$x-9=0$
Add 9 to both sides.
$x=9$
