X^2+8x+11=0 which number would have to be added to complete the square

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?

How can constraints be used to model a real-world situation?

If the square of a positive integer is added to 2 times the integer the result is 48. find the integer.