Suppose that during a speech, (x - 4) 2 students protested. If 36 students protested, what are the possible values of x?

The expression will become;

(x - 4) ² = 36

Now by using the formula;

(a-b) ² = a² - 2ab + b²

(x - 4) ² = x² - 2 (x) (4) + 4² = x² - 8x + 16

Now the expression will be;

x² - 8x + 16 = 36

x² - 8x + 16 - 36 = 0

x² - 8x - 20 = 0

Now by using factorization method;

x² - 10x + 2x - 20 = 0, - 10 + 2 = 8 and - 10 x 2 = - 20

x (x-10) + 2 (x - 10) = 0

(x - 10) (x + 2) = 0

Now either x - 10 = 0 or x+2 = 0

it means x = 10 or x - 2

So, the possible values of x are 10 and - 2.