The square of one integer is 55 less than the square of the next consecutive integer. Find the lesser integer.
Let x = the lesser integer and let x + 1 = the greater integer. The sentence, "The square of one integer is 55 less than the square of the further consecutive integer," can translate to the equation x2 = (x + 1)2 -55. Multiply the binomial (x + 1)2 as (x + 1)(x + 1) by using the distributive property: x2 = x2 + 1x + 1x + 1 - 55. Combine such as terms: x2 = x2 + 2x - 54. Subtract x2 from both sides of the equation: x2 - x2 = x2 - x2 + 2x - 54. Add 54 to both sides of the equation: 0 + 54 = 2x - 54 + 54. Divide both sides through 2: 54/2 = 2x/2. The variable is now alone: 27 = x. The lesser integer is 27.