6 times a number is 16 less than the square of that number. Find the negative solution.

Answer 1

A quadratic is applicable here given

6n = n² - 16

Set up the quadratic by subtracting 6n from both sides of the equation:

0 = n² - 6n - 16

Factoring

(n - 8)(n + 2)=0

The negative solution is n = -2

Checking in the original set up we have

6(-2) = (-2)² - 16

-12 = 4 - 16

-12 = -12

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