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.

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