The sum of the square of a number and 12 times the number is -27. What is the smaller probable value of this number?
Let x = the number. The statement that is "The sum of the square of a number and 12 times the number is -27," translates to the equation x^{2} + 12x = -27. Put the equation in standard creates and set it equal to zero: x^{2} + 12x + 27 = 0. Factor the left side of the equation: (x + 3)(x + 9) = 0. Set every factor equal to zero and solve: x + 3 = 0 or x + 9 = 0; x = -3 or x = -9. The possible values of this number are -3 or -9, the smaller of that is -9.