Question

The difference of the square of a number and 28 is equal to three times that number find the negative solution

Answer 1

The negative solution = x = -4

Explanation:

Let the number be = x

The square of number = x²

The difference between the square of a number and 28 = x²-28

Given that the difference of the square of a number and 28 is equal to three times that number.

Thus, the equation becomes

`x^2-28=3x`

subtract 3x from both sides

`x^2-28-3x=3x-3x`

`x^2-3x-28=0`

`\left(x+4\right)\left(x-7\right)=0`

`x+4=0\quad \mathrm{or}\quad \:x-7=0`

`x=-4,\:x=7`

Thus, the negative solution = x = -4