The square of a positive integer minus twice its consecutive integer is equal to 22. find the intege

The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers.

Let x = the original positive integer. We have:

• Consecutive integer is x + 1
• x^2 - 2(x + 1) = 22

Multiply through:
x^2 - 2x - 2 = 22

Subtract 22 from each side:
x^2 - 2x - 24 = 0

Using our quadratic calculator, we get:
x = 6 and x = -4

Since the problem states positive integers, we use:
x = 6 and x + 1 = 7
(6, 7)