The problem provided involves two consecutive positive integers, where the square of the second integer added to six times the first integer equals 85. We are tasked with setting up the correct equation for this word problem.

Let’s define the two consecutive integers:

• First integer: $x$
• Second integer: $x + 1$

According to the problem, the equation should be:

$6x + (x + 1)^2 = 85$

This equation states that 6 times the first integer ($x$) plus the square of the second integer ($(x + 1)^2$) is equal to 85.

The correct answer is:

$6x + (x + 1)^2 = 85$

This matches the option you have selected in the image.

Would you like further explanation on how to solve this equation? Here are some related questions to consider:

1. What steps would you take to solve the equation $6x + (x + 1)^2 = 85$?
2. How do we expand the term $(x + 1)^2$?
3. What are consecutive integers, and why does the second integer equal $x + 1$?
4. How can we verify the solution to this equation once found?
5. What other types of problems involve consecutive integers?

Tip: When solving equations involving squares, always check for extraneous solutions by plugging the result back into the original equation.