Given: A statement, "When 27 is subtracted from the square of a
number, the result is 6 times the number."
Required: To determine the number.
Explanation: Let the number be x. Then according to the question-
[tex]x^2-27=6x[/tex]Rearranging the equation as -
[tex]x^2-6x-27=0[/tex]The quadratic equation can be simplified as follows-
[tex]\begin{gathered} x^2-9x+3x-27=0 \\ x(x-9)+3(x-9)=0 \\ (x+3)(x-9)=0 \\ x=-3\text{ or }x=9 \end{gathered}[/tex]Final Answer: The negative solution is-
[tex]x=-3[/tex]