Question

When 27 is subtracted from the square of anumber, the result is 6 times the number. Findthe negative solution.

Answer 1

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-

$x^2-27=6x$

Rearranging the equation as -

$x^2-6x-27=0$

The quadratic equation can be simplified as follows-

$\begin{gathered} x^2-9x+3x-27=0 \\ x(x-9)+3(x-9)=0 \\ (x+3)(x-9)=0 \\ x=-3\text{ or }x=9 \end{gathered}$

Final Answer: The negative solution is-

$x=-3$