The product of two consecutive negative integers is 2550. What is the sum of the two integers?
I want to find two consecutive negative integers, x and x+1, such that x(x+1) = 2550. Instead, I notice that x(x+1) is always an even number, because either x or x+1 is even. So I can divide both sides of the equation by 2 and get x(x+1)/2 = 1275. Now I have a smaller number to factor, and I see that 1275 = 25 * 51. So x(x+1) = 50 * 51. This means that either x = 50 and x+1 = 51, or x = -51 and x+1 = -50. Since I want negative integers, I choose the second option. So x = -51 and x+1 = -50. The sum of the two integers is x + (x+1) = -51 + (-50) = -101. 