Answer:
x = 24 or 7
Step-by-step explanation:
Given a number is subtracted from 18 and 13.
Let us call this number [tex]$ x $[/tex].
From the given data we have [tex]$ x -18 $[/tex] and [tex]$ x - 13 $[/tex].
The product of these two numbers is [tex]$ (x - 18) (x - 13) = 66 $[/tex].
This leads us to the quadratic equation, mentioned in the question.
[tex]$ \implies x^2 -13x -18x +(13)(18) = 66 $[/tex].
[tex]$ \implies x^2 - 31x + 168 = 0 $[/tex]
Solving for [tex]$ x $[/tex] we get [tex]$ x =24 $ or $x = 7$[/tex]