Let's call Aubrey's age x and Chase's age y.
Since the ages are consecutive integers, y = x - 1.
Since the product of their ages is 56, x * y = x * (x - 1) = 56.
Expanding the right side of the equation gives x^2 - x = 56.
Adding x to both sides of the equation gives x^2 = x + 56.
Subtracting 56 from both sides of the equation gives x^2 - x - 56 = 0.
This is a quadratic equation, and it can be solved using the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
Where a, b, and c are the coefficients of the quadratic equation:
a = 1, b = -1, c = -56
Plugging these values into the formula gives:
x = (1 +/- sqrt(1^2 - 41(-56))) / 2*1
= (1 +/- sqrt(1 + 224)) / 2
= (1 +/- 15) / 2
The two solutions of the equation are x = -14 and x = 8.
Since Aubrey's age must be positive, Aubrey's age is x = 8.
Therefore, Aubrey is 8 years old and Chase is 7 years old.