Question

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

Answer 1

The negative solution is -2

Explanation:

Let the number be x

From the question we can deduce the equation below;

`x^(2)- 16 = 6x`

Solving the quadratic equation by factorization;

`x^(2)- 16 - 6x = 0`

`x^(2) - 6x - 16 = 0`

the factors of the quadratic equation are -8 and 2

`x^(2) - 8x + 2x - 16 = 0`

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

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

Therefore, x = -2 or 8

The negative solution is -2.

PROOF;

`x^(2)- 16 = 6x`

[-2]^2 - 16 = 6(-2)

4 - 16 = -12

-12 = -12