The difference of the squares of two positive consecutive even integers is 76. find the integers. use the fact that, if x represents an even integer, then x+2 represents the next consecutive even integer.

Write an equation based on the problem
(x + 2)² - x² = 76

We should find the value of x to know the smaller integer.
(x + 2)² - x² = 76
simplify the quadratic expression for (x + 2)²
(x + 2)² - x² = 76
(x + 2)(x + 2) - x² = 76
x² + 2x + 2x + 4 - x² = 76
x² - x² + 4x + 4 = 76
4x + 4 = 76

Solve for x
4x = 76 - 4
4x = 72
  x = 72/4
  x = 18

Find the bigger integer
x + 2 = 18 + 2 = 20

The integers are 18 and 20