South African Mathematics Olympiad

Question

The values of x satisfying the equation (x - 7)(x + 12) = -48 are (A) 7 or 12 (B) -7 or 12 (C) 4 or -9 (D) -4 or 9 (E) -12 or 7

Accepted Answer

Multiplying out the equation gives x^2 + 5x - 84 = -48, so x^2 + 5x - 36 = 0. This factorizes to (x + 9)(x - 4) = 0, so x = -9 or x = +4.